Einstein, the searcher : his work explained from dialogues with Einstein

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EINSTEIN THE SEARCHER

EINSTEIN
THE SEARCHER

HIS WORK EXPLAINED FROM
DIALOGUES WITH EINSTEIN

BY

ALEXANDER MOSZKOWSKI

TRANSLATED BY

HENRY L. BROSE

METHUEN & GO. LTD.

36 ESSEX STREET W.G.

LONDON

First Published in 1^21

6

EXTRACT FROM THE AUTHOR'S
PREFACE

THE book which is herewith presented to the public
has few contemporaries of a Uke nature ; it deserves
special attention inasmuch as it is illuminated by the
name Albert Einstein, and deals with a personality whose
achievements mark a turning-point in the development of
science.

Every investigator, who enlarges our vision by some
permanent discovery, becomes a milestone on the road to
knowledge, and great would be the array of those who have
defined the stages of the long avenue of research. One might
endeavour, then, to decide to whom mankind owes the greater
debt, to EucHd or to Archimedes, to Plato or to Aristotle, to
Descartes or to Pascal, to Lagrange or to Gauss, to Kepler
or to Copernicus. One would have to investigate — as far as
this is possible — in how far each outstanding personahty was
in advance of his time, whether some contemporary might
not have had the equal good fortune to stumble on the same
discovery, and whether, indeed, the time had not come when
it must inevitably have been revealed. If we then further
selected only those who saw far beyond their own age into the
ilHmitable future of knowledge, this great number of celebrities
would be considerably diminished. We should glance away
from the milestones, and fix our gaze on the larger signs that
denote the lines of demarcation of the sciences, and among
them we should find the name of Albert Einstein. We may
find it necessary to proceed to a still more rigorous classifica-

vi EINSTEIN THE SEARCHER

tion ; Science, herself, may rearrange her chronological table
later, and reckon the time at which Einstein's doctrine first
appeared as the beginning of an important era.

This would in itself justify — ^nay, render imperative — the
writing of a book about Einstein. But this need has already
been satisfied on several occasions, and there is even now a
considerable amount of literature about him. At the end of
this generation we shall possess a voluminous library com-
posed entirely of books about Einstein. The present book
will differ from most of these, in that Einstein here occurs not
only objectively but also subjectively. We shall, of course,
speak of him here too, but we shall also hear him speak him-
self, and there can be no doubt that all who are devoted to the
world thought can but gain by listening to him.

The title agrees with the circumstance to which this book
owes its birth. And in undertaking to address itself to the
circle of readers as to an audience, it promises much eloquence
that came from Einstein's own hps, during hours of social
intercourse, far removed from academic purposes and not
based on any definite scheme intended for instruction. It
will, therefore, be neither a course of lectures nor anything
similar aiming at a systematic order and development. Nor is
it a mere phonographic record, for this is made impossible if
for no other reason than that whoever has the good fortune to
converse with tliis man, finds every minute far too precious
to waste it in snatching moments to take shorthand notes.
What he has heard and discussed crystallizes itself in sub-
sequent notes, and to some extent he relies on his memory,
which would have to be extraordinarily lax if it managed to
forget the essentials of such conversations.

But these essentials could not be attained by clinging
closely to the exact terms of utterance. This would be a gain
neither for the scheme of the book nor for the reader who
wishes to follow a great thinker in all the ramifications of his
ideas. It must be reiterated that this book is intended neither

EXTRACT FROM THE AUTHOR'S PREFACE vii

as a textbook nor as a guide leading to a complete system of
thought ; nor, above all, is it in any way due to Einstein, nor
desired by him. Any value and attraction of the book is
rather to be sought in its kaleidoscopic nature, its loose con-
nexion, which expresses a general meaning without being
narrowed to pedantic Hmits by a restriction to literal re-
petition. It is just this absence of the method that is rightly
demanded of a textbook, which may enable these conversa-
tions to pass on to the world a Httle of the pleasure which they
originally gave me. Perhaps they will even be sufficient to
furnish the reader with a picture of the eminent scientist,
sufficient to give him a glimpse of his personality, without
demanding a detailed study to secure this end. Even here
I should like to state that the range of Einstein's genius
extends much further than is generally surmised by those who
have busied themselves only with the actual physical theory.
It sends out rays in all directions, and brings into view
wonderful cosmic features imder his stimulus — features which
are, of course, embedded in the very refractory mathematical
shell of his physics which embraces the whole world. But
only minds of the distant future, perhaps, will be in a position
to realize that all our mental knowledge is illuminated by the
light of his doctrine.

Einstein's mission is that of a king who is pursuing build-
ing operations on a large scale ; carters and workmen, each
in their own Une, receive employment for decades ahead.
But apart from the technical work, there may still be room
for non-technical account, which, without following a definite
programme, yet pursues a definite object, to offer Einsteiniana
in an easily intelHgible and ever-changing form, to represent
him, as it were, wandering over fields and meadows, and every
now and then stooping to pluck some problem in the guise of a
flower. Seeing that he granted me the pleasure of accompany-
ing him on these excursions, it was not within my sphere to
expect in addition that he would direct his steps according to

viii EINSTEIN THE SEARCHER

a preconceived plan. Often enough the goal vanished, and
there remained nothing but the pleasure of the rambles them-
selves with the consciousness of their purpose. As Schopen-
hauer remarks, one who walks for leisure can never be said to
be making detours ; and this holds true independently of the
nature of the country that happens to be traversed at the
moment. It I just now mentioned walks on meadowy slopes,
this is not to be understood Uterally. In Einstein'? company
one encounters from moment to moment quite suddenly some
adventure which destroys our comparison with idylHc rambles.
Abysmal depths appear, and one has to pass along dangerous
pathways. It is at these moments that unexpected views
present themselves, and many strips of landscape that, accord-
ing to our previous estimate, appeared to be situated on higher
slopes, are now discovered reposing far below. We are
familiar with the " Wanderer Fantasie " of Schubert ; its tonal
disposition is realistic, conforming to Nature, yet its general
expression is transcendental : so is a ramble with Einstein ;
he remains firmly implanted in reahty, but the distant views
that he points out stretch into transcendental regions. He
seems to me to be essentially as much an artist as a discoverer,
and if some sense of this heaven-sent combination of gifts
should be inspired by this book, it alone would justify the
pubUcation of these talks.

TRANSLATOR'S NOTE

IT is scarcely necessary to enlarge on the scope and design
of the present book, which manifest themselves at a
glance.

The author merits our thanks for making accessible to us
material about Einstein which, in the ordinary course of events,
would ever remain unknown. An account of Einstein's work
would be incomplete without a sketch of his personality.
Mr. Moszkowski invites us to ramble with Einstein into realms
not confined to pure physics. Many subjects that have a
peculiar interest at the present critical stage of the world's
history receive illuminating attention. It is hoped that the
appearance of the book in English will stimulate further
interest in the thought- world of a great scientist.

Warm thanks are due to Mr. Raymond Kershaw, B.A.,

and to my sister, Miss Hilda Brose, for help in reading the

manuscript and the proofs.

HENRY L. BROSE

Oxford, 1921

CONTENTS

CHAP.

I. Phenomena in the Heavens
II. Beyond our Power

III. Valhalla .

IV. Education
V. The Discoverer

VI. Of Different Worlds
VII. Problems .
VIII. Highways and By-ways
IX. An Experimental Analogy
X. Disconnected Suggestions
XI. Einstein's Life and Personality
Index ....

PAGB

I

20

38
62

88
115
143
172
192

2(X)
220

245

EINSTEIN THE SEARCHER

CHAPTER I
PHENOMENA IN THE HEAVENS

'■ Proclamation of the New Mechanics. — 'Verification of Theoretical Results.
— Parallels with Leverrier, — Neptune and Mercury. — Testing the Theory of
Relativity. — ^The Solar Eclipse of 191 9. — The Programme of an Expedition.
— The Curved Ray of Light. — Refinement of Calculation and Measurement. —
Stellar Photography. — The Principle of Equivalence. — The Sun Myth.

ON the 13th October 1910 a memorable event took
place in the Berlin Scientific Association : Henri
Poincar6, the eminent physicist and mathematician,
had been announced to give a lecture in the rooms of the
institute " Urania " ; an audience of rather meagre dimensions
assembled. I still see him before me in my mind's eye, a
scholar who was snatched away in the prime of his creative
period, a man whose external appearance did not suggest the
light of genius, and whose carefully trimmed beard reminded
one rather of the type of a practising barrister. He walked
up and down the platform, accompanying his speech with
gestures marked by an easy elegance. There was no sign of
an attempt to force a doctrine. He developed his thesis, in
spite of the foreign language, in fluent and readily intelligible
terms.

It was at this lecture that we heard the name Albert
Einstein pronounced for the first time.

Poincare's address was on the New Mechanics, and was
intended to make us acquainted with the beginning of a
tendency which, he himself confessed, had violently dis-
turbed the equihbrium of his former fundamental views. He
repeatedly broke the usually even flow of his voice to indicate,
with an emphatic gesture, that we had perhaps arrived at a

2 EINSTEIN THE SEARCHER

critical, nay epochal, point marking the commencement of a
new era of thought.

'* Perhaps " was a word he never failed to emphasize.
He persistently laid stress on his doubts, differentiated between
hardened facts and hypotheses, still clinging to the hope that
the new doctrine he was expounding would yet admit of an
avenue leading back to the older views. This revolution, so
he said, seemed to threaten things in science which a short
while ago were looked upon as absolutely certain, namely,
fundamental theorems of classical mechanics, for which we
are indebted to the genius of Newton. For the present this
revolution is of course only a threatening spectre, for it is
quite possible that, sooner or later, the old established
dynamical principles of Newton will emerge victoriously.
Later in the course of his lecture he declared repeatedly that
he felt a diffidence akin to fear at the sight of the accumulating
number of hypotheses, and that it seemed to border on the
impossible to attempt to arrange them into a system.

It is a matter of complete indifference how the revelations
of Poincar^ affected us individually ; if I may infer from my
own case, there is only one word to express it — staggering !
Obhvious of the doubts of the lecturer, I was swept along under
the impetus of this new and mighty current of thought. This
awakened two wishes in me : to become acquainted with
Einstein's researches as far as lay within my power, and, if
possible, to see him once in person. In me the abstract had
become inseparable from the concrete personal element.
The presentiment of the happy moment in the future hovered
before my vision, whispering that I should hear his doctrine
from his own lips.

Several years later Einstein was appointed professor of
the Academy of Sciences with the right of lecturing at the
University of Berlin. This brought my personal wish within
reach. Trusting to good fortune, I set about materiaUzing it.
In conjunction with a colleague I wrote him a letter asking
him to honour with his presence one of the informal evenings
instituted by our Literary Society at the Hotel Bristol. Here
he was my neighbour at table, and chatted with me for some
hours. Nowadays his appearance is known to every one
through the innumerable photos which have appeared in the

PHENOMENA IN THE HEAVENS 8

papers. At that time I had never seen his countenance before,
and I became absorbed in studying his features, which struck
me as being those of a kindly, artistically inclined, being, in
nowise suggesting a professor. He seemed vivacious and un-
restrained in conversation, and, in response to our request,
willingly touched upon his own subject as far as the place and
occasion allowed, exemplif5dng Horace's saying, " Omne tulit
punctum, qui miscuit utile dulci, tironem delectando pari-
terque monendo.'* It was certainly most delightful. Yet at
moments I was reminded of a male sphinx, suggested by his
highly expressive enigmatic forehead. Even now, after a
warm acquaintanceship stretching over years, I cannot shake
off this impression. It often overcomes me in the midst of a
pleasant conversation interspersed with jests whilst enjo5dng
a cigar after tea ; I suddenly feel the mysterious sway of a
subtle intellect which captivates and yet baffles the mind.

At that time, early in 1916, only a few members of the
Literary Society divined who it was that was enjoying their
hospitality. In the eyes of Berlin, Einstein's star was be-
ginning its upward course, but was still too near the horizon to
be visible generally. My own vision, sharpened by the French
lecture and by a friend who was a physicist, anticipated events,
and already saw Einstein's star at its zenith, although I was
not even aware at that time that Poincar^ had in the mean-
time overcome his doubts and had fully recognized the
lasting importance of Einstein's researches. I had the
instinctive feeUng that I was sitting next to a Galilei. The
fanfares sounded in the following years as a sign of apprecia-
tion by his contemporaries were only a fuller instrumentation
of the music of destiny which had vibrated in my ears ever
since that time.

I recollect one little incident : one of these lovers of
literature, who was, however, totally ignorant of natural
science, had accidentally seen several learned articles deahng
with Einstein's Reports for the Academy, and had preserved
the cuttings in his pocket-book. He considered this a fitting
opportunity for enUghtenment. Surely a brief question
would suffice to guide one through these intricate channels.
*' Professor, will you kindly tell me the meaning of potential,
invariant, contra variant, energy-tensor, scalar, relativity-

4 EINSTEIN THE SEARCHER

postulate, hyper-Euclidean, and inertial system ? Can you
explain them to me in a few words ? " — " Certainly," said
Einstein, '* those are merely technical expressions ! " That
was the end of the little lesson.

Far into the night three of us sat in a caf6 while Einstein
gently lifted the veil from his newest discovery for the benefit
of my journalist friend and myself. We gathered from his
remarks that a Special Theory of Relativity formed a prelude
to a general theory which embraced the problem of gravita-
tion in its widest sense, and hence also the physical constitu-
tion of the world. What interested me apart from this theme,
which was, of course, only touched upon Ughtly, was the
personal question in its psychological aspect.

" Professor," said I, " such investigations must involve
enormous mental excitement. I imagine that there lurks
behind every solved problem ever and again some new problem
with a threatening or a fascinating aspect, as the case may be,
each one caUing up a tumult of emotion in its author. How
do you succeed in mastering this difficulty ? Are you not
continually tormented by restless thoughts that noisily invade
your dreams ? Do you ever succeed at all in enjoying undis-
turbed slumber ? "

The very tone in which the answer was given showed
clearly how free he felt himself of such nervous troubles which
usually oppress even the mediocre thinker. It is fortunate that
such affections do not penetrate to his high level. " I break
off whenever I wish," he said, " and banish all difficulties when
the hour for sleep arrives. Thinking during dreams, as in the
case of artists, such as poets and composers, by which they
weave the thread of day on into the night, is quite foreign to me.
Nevertheless, I must confess that at the very beginning, when
the special theory of relativity began to germinate in me, I was
visited by all sorts of nervous conflicts. When young I used
to go away for weeks in a state of confusion, as one who at that
time had yet to overcome the stage of stupefaction in his first
encounter with such questions. Things have changed since
then, and I can assure you that there is no need to worry about
my rest."

" Notwithstanding," I answered, " cases may arise in
which a certain result is to be verified by observation and

PHENOMENA IN THE HEAVENS ^

experiment. This might easily give rise to nerve-racking
experiences. If, for instance, a theory leads to a calculation
which does not agree with reality, the propounder must surely
feel considerably oppressed by this mere possibiUty. Let us
take a particular event. I have heard that you have made a
new calculation of the path of the planet Mercury on the
basis of your doctrine. This must certainly have been a
laborious and involved piece of work. You were firmly con-
vinced of the theory, perhaps you alone. It had not yet been
verified by an actual fact. In such cases conditions of great
psychological tension must surely assert themselves. What in
Heaven's name will happen if the expected result does not
appear ? What if it contradicts the theory ? The effect on
the founder of the theory cannot even be imagined ! "

" Such questions,'* said Einstein, " did not lie in my path.
That result could not be otherwise than right. I was only
concerned in putting the result into a lucid form. I did not
for one second doubt that it would agree with observation.
There was no sense in getting excited about what was self-
evident."

Let us now consider several facts of natural science, apart
from this chat, but suggested by it, which caused Einstein little
excitement, but the whole world generally, so much the more.
By way of illustration we shall link them up with the result of
a forerunner who, like Einstein, fixed on paper what should
happen in the heavens.

Formerly, whenever one wished to play a particularly
effective trump card in favour of research work it was cus-
tomary to quote the achievement of the French astronomer
Leverrier who, pen in hand, established the material existence
of a planet at that time quite unknown and unnoticed. Certain
disturbances in the orbit of the planet Uranus, which was
regarded as being the most distant of the wandering stars, at
that time had caused him to believe in the certainty of the
existence of a still more distant planet, and by using merely
the theoretical methods of celestial mechanics in connexion
with the problem of three bodies he succeeded in revealing
what was hidden behind the visible constellations. He reported
the result of his calculations to the Berlin Observatory about
seventy-five years ago, as it was at that time in possession of

6 EINSTEIN THE SEARCHER

the best instruments. It was then that the amazing event
happened : on the very same evening an observer in Berlin,
Gottfried Galle, discovered the predicted new star almost
exactly at the point of the heavens for which it was prophesied,
only half the moon's diameter from it. The new planet
Neptune, the farthest outpost of our solar system, reposed as
a prisoner in his telescope ; the seemingly undiscoverable star
had capitulated in the face of mental efforts of a mathematical
scholar, who, in reasoning meditation, had sketched his curves
in the quiet atmosphere of his study.

This was certainly bewildering enough, but nevertheless
this incredible result which stirred the imagination so strongly
was directly rooted in reaUty, lay on the path of research,
followed of necessity from the laws of motion known at that
time, and disclosed itself as a new proof of the doctrines of
astronomy which had long been recognized as supreme and
incontestable. Leverrier had not created these, but had found
them ready ; he applied them with the mind of genius. Any-
one who nowadays is sufficiently trained to work through the
highly compUcated calculation of Leverrier has every reason
to marvel at a work which is entirely mathematical throughout.

Our own times have been marked by an event of still greater
significance.

Irregularities had shown themselves in observation of the
heavens that could not be explained or grasped by the
accepted methods of classical mechanics. To interpret them,
ideas of a revolutionary nature were necessary. Man's view of
the plan according to which the universe is mapped out had
to be radically reformed to bring within comprehension the
problems that presented themselves in macroscopic as well as
in microscopic regions, in the courses of the stars as well as in
the motions of the ultimate constituents of the atom of material
bodies, incapable of being directly observed. The goal con-
sisted in bringing those doctrines in which truth had been
proclaimed in its essential features, but not exhaustively, by
the genius of Copernicus, GaHlei, Kepler, and Newton, to their
conclusion by penetrating as far as possible into the mysteries of
the structure of the universe. This is where Einstein comes
forward.

Whereas the outermost planet Neptune had bowed to the

PHENOMENA IN THE HEAVENS 7

accepted laws, by merely disclosing his presence^ Mercury, the
innermost planet, preserved an obstinate attitude even in the
face of the most refined calculations. These always led to
an unaccountable remainder, a disagreement, which seemed
very small when expressed in numbers and words, and yet
enclosed a deep secret. Wherein did this disagreement
consist ? In a difference of arc which had likewise been dis-
covered by Leverrier and which defied explanation. It was
only a matter of about forty-five insignificant quantities,
seconds of arc, which seemed vanishingly small since this
deviation did not occur within a month or a year, but was
spread over a whole century. By just so much, or rather so
little, the rotation of Mercury's orbit differed from what might
be termed the allowable astronomical value. Observation was
exact, calculation was exact ; why, then, the discrepancy ?

It was thus inferred that there was stiU some hidden un-
explored factor which had to be taken into account in the
fundamental principles of celestial mechanics. The formerly
invisible Neptune confirmed the old rule by appearing.
Mercury, which was visible, opposed the rule.

In 1 9 10 Poincare had touched upon this embarrassing
question, mentioning that here was a possibility of testing
the new mechanics.

He declined the suggestion of some astronomers that this
was again a Leverrier problem and that there must exist another
undiscovered planet still nearer the sun and disturbing
Mercury's orbit. He also refused to accept the assumption
that the disturbance might be caused by a ring of cosmic
matter distributed round the sun. Poincard divined that the
new mechanics could supply the key to the enigma, but,
obviously to be quite conscientious, he expressed his presenti-
ment in very cautious terms. On that occasion he said that
some special cause had yet to be found to explain the anomaly
of Mercury's behaviour ; till that was discovered one could
only say that the new doctrine could not be regarded as in
contradiction to astronomical facts. But the true explanation
was gradually drawing near. Five years later, on i8th Nov-
ember 1915, Albert Einstein presented to the Prussian Academy
of Sciences a paper which solved this riddle which, expressed in
seconds, seemed so insignificant and yet was of such enormous

8 EINSTEIN THE SEARCHER

importance in its bearing on fundamental questions. He
proved the problem was solved quite accurately if the general
Theory of Relativity he had founded was accepted as the only
valid basis for the phenomena of cosmic motions.

Many would at this point express a wish to have the
essence of the doctrine of relativity explained in an easily
intelligible manner. Indeed, some would go even further in
their desire, and would ask for a simple description in a few
succinct sentences. This, measured in terms of difficulty and
possibihty, would be about equivalent to wishing to learn the
history of the world by reading several quarto pages of manu-
script or a novelette. But even if we start at long range and
use elaborate materials for our description, we should have to
give up the idea that this knowledge may be gained with
playful ease. For this doctrine, inasmuch as it discloses the
relationship between mathematical and physical events,
emerges out of mathematics, which thus limits the mode of its
representation. Whoever undertakes to present it in a form
in which it is easily intelligible, that is quite unmathematical
and yet complete, is engaged in an impossible venture ; he is
like one who would whistle Kepler's Laws on the flute or would
elucidate Kant's Critique of Pure Reason by means of coloured
illustrations. In all frankness we must confess once and for
all that whenever popular accounts are attempted they can be
only in the nature of vague suggestions removed from the
domain of mathematics. But even such indications have a
fruitful result if they succeed in focusing the attention of the
reader or the hearer so that the connexions, the Leitmotivs,
so to speak, of the doctrine, are at least suggested.

It must therefore suffice if we place the conception of
approximation in the foreground here as in other parts of
this book. Till quite recently Newton's Equations of Motion
were used as a foundation for verifying astronomical occur-
rences. These are symbolical representations expressed as
formulae that contain in an exceedingly simple form the law
of mass attraction. They express the comprehensive principle
that the attraction is directly proportional to the mass and
inversely proportional to the square of the distance ; so that
the moving force is doubled when the mass is doubled, whereas
if the distance is double, the force is only a quarter as great.

PHENOMENA IN THE HEAVENS 9

if the distance is trebled, the force becomes one-ninth as
great.

According to the Theory of Relativity this fundamental
law is not wrong or invalid, but no longer holds fully if pursued
to its last inferences. In appl3dng corrections to it, new
factors occur, such as the ratio of given velocities to the
velocity of light, and the new geometry which operates with
** world-hnes " in space which, amalgamated with the dimen-
sion of time, is regarded as a quadruply extended continuum.
Einstein has actually supplemented these fundamental
equations for the motion of masses so that the original form
states the true condition of affairs only approximately, where-
as Einstein's equations give the motion with very great
accuracy.

The above-mentioned essay of Einstein is carried out as
if the structure bequeathed to us by Newton required the
addition of a final, very delicate pinnacle. For the mathe-
matician this pinnacle is given as a combination of signs,
representing a so-called " ElHptic Interval." Such an in-
terval is a very weird construction, and the man who will
make it apprehended by the general reader is yet to be born.
When Lord Byron said :

" And Coleridge, too, has lately taken wing.
But like a hawk encumbered with his hood, —
Explaining Metaphysics to the nation —
/ wish he would explain his Explanation."

{Dedication to "Don Juan")

he had still a sure footing in inteUigibihty, compared with
the non-mathematician, who demands an explanation for
such a construction. And what a complex of mathematical
dangers must be overcome even before the question of the
meaning of this integral is crystallized out I

But now the explanation had arrived and could be evalu-
ated, if only approximately. Before we give the result, let
us just describe at least one technical term, namely, " Peri-
hehon.'* It is that point of a planet ory orbit which Hes
nearest the sun. This orbit is an ellipse, that is, an elongated
curved Une in the interior of which one distinguishes a major
axis in the direction of elongation, and a minor axis perpen-
dicular to the former at its middle point. The perihelion

10 EINSTEIN THE SEARCHER

of a planet ory orbit is at one of the end points of the major
axis.

In time the periheUon alters its position in space, ad-
vancing in the same sense as the orbit is traversed. It would
naturally be assumed that the amount of this advance as
measured astronomically would agree with the calculation
resulting from Newton's theory. But this was not the case.
An unaccountable remainder was left over, which astronomers
ascertained to be 45 seconds (of arc) per 100 years, with a
possible fluctuation of plus or minus 5 seconds. Thus, if the
new result were found to lie between 40 and 50 seconds, the
new theory would henceforth have to be regarded as the only
valid one.

It happened just as Einstein predicted : calculation accord-
ing to his theory shows that for the planet Mercury the peri-
helion should advance 43 seconds per 100 years. This
signifies full agreement with observation and fully removes
the former apparent difficulty. Whereas Leverrier in his
time had pointed out a new planet, Einstein brought to view
something far more important : a new truth.

It was a test of accuracy so dazzHng that it alone would
have sufficed to prove the correctness of Einstein's Principles.
Yet, a second test, fraught with graver and more far-reaching
consequences, presented itself — a test which could be apphed
only several years later, and which developed into a scientific
event of the highest importance.

For at the same time that Einstein solved the problem of
Mercury, he had investigated the path of Hght-rays according to
his revolutionary method, and had arrived at the conclusion
that every ray under the influence of a gravitational field,
as, for example, in the neighbourhood of the sun, must become
curved. This daring announcement gave a new possibility of
putting the theory to a practical test during the total echpse
of the sun on 29th May 1919. For, when the disc of the sun is
obscured, the stars that are closest to it become visible (even
to the naked eye). They may be photographed, and the
distances of the points of Hght on the negative allow us to
detect whether the rays from the stars in passing the massive
body of the sun have actually been deflected by the amount
prophesied by Einstein.

PHENOMENA IN THE HEAVENS 11

Once again current thought encountered a sharp comer,
and " common sense/* which furnishes its own certificate of
merit, threatened to become rebellious. How now ? A ray
from a star could be curved ? Does not this contradict the
elementary conception of the straight Hues, that is, the shortest
lines, for which we have no better picture than just these rays ?
Did not Leonardo da Vinci define the straight line by means of
the term linea radiosa.

But such supposedly self-evident facts have no longer a
place in the space-time world. The point was to test whether
a physical anomaly which had been predicted actually
existed. If the deflection of the rays really happened, it
should manifest itself in the distances between the stars on
the photographic plate being greater than one would expect
from their actual position.

For the curvature has its concave side towards the sun,
as is easy to see, once the phenomenon is regarded as possible.
It is as if the ray were directly subject to gravitation. Let us
take two stars, one on each side of the sun. On account of
the concavities the eye receives rays from them under a greater
visual angle than if the rays were straight, and interprets this
angle as denoting a greater distance between the sources of
Hght, that is, it sees the two stars farther apart than in the case
of rectilinear propagation.

By how much farther apart ? The preceding calculation
and the subsequent direct observation demanded incredible
deUcacy of measurement. If we suppose the whole arc of the
heavens divided into easily picturable units such as degrees,
then the apparent width of the moon is about half a degree.
We may still easily imagine the thirtieth part of this, namely, a
minute of arc. But the sixtieth part of the latter, the second
of arc, vanishes almost out of the range of sense-perception.
And it was just this minute measure that came into question,
for the theory which had been developed from pure thought
predicted a deflection of ly^^ seconds of arc. This corresponds
to about a hairbreadth when seen at a distance of 17 yards,
or to the thickness of a match at a distance of over half a
mile.

One of the greatest problems of the. most comprehensive
science depended on this unthinkably small measure.

12 EINSTEIN THE SEARCHER

In no sense did Einstein himself entertain a possibility of
doubt.

On repeated occasions before May 1919 I had opportunities
of questioning him on this point. There was no shadow of a
scruple, no ominous fears clouded his anticipations. Yet
great things were at stake.

Observation was to show " the correctness of Einstein's
world system " by a fact clearly intelligible to the whole world,
one depending on a very sensitive test of less than two seconds
of arc.

" But, Professor/' said I, on various occasions, " what if it
turns out to be more or less ? These things are dependent on
apparatus that may be faulty, or on unforeseen imperfections
of observation." A smile was Einstein's only answer, and this
smile expressed his unshakeable faith in the instruments and
the observers to whom this duty was to be entrusted.

Moreover, it is to be remarked that no great lengths of time
were available for comfortable experimentation in taking this
photographic record. For the greatest possible duration of a
total echpse of the sun viewed at a definite place amounts to
less than eight minutes, so that there was no room for mishaps
in this short space of time, nor must any intervening cloud
appear. The kindly co-operation of the heavens was indis-
pensable— and was not refused. The sun, in this case the
darkened sun, brought this fact to hght.

Two EngUsh expeditions had been equipped for the special
occasion of the echpse — one to proceed to Sobral and the other
to the Island of Principe, off Portuguese Africa ; they were
sent officially with equipment provided in the main by the
time-honoured Royal Society. Considering the times, it was
regarded as the first symptom of the revival of international
science, a praiseworthy undertaking. A huge apparatus was
set into motion for a purely scientific object with not the
shghtest relation to any purpose useful in practical Hfe. It
was a highly technical investigation whose real significance
could be grasped by only very few minds. Yet interest was
excited in circles reaching far beyond that of the professional
scientist. As the solar eclipse approached, the consciousness
of amateurs became stirred with indefinite ideas of cosmic
phenomena. And just as the navigator gazes at the Polar

PHENOMENA IN THE HEAVENS 18

Star, so men directed their attention to the constellation of
Einstein, which was not yet depicted in stellar maps, but, from
which something uncomprehended, but undoubtedly very
important, was to blaze forth.

In June it was announced that the star photographs had
been successful in most cases, yet for weeks, nay for months,
we had to exercise patience. For the photographs, although
they required little time to be taken, took much longer to
develop and, above all, to be measured ; in view of the order of
smallness of the distances to be compared, this was a difficult
and troublesome task, for the points of light on the plate did
not answer immediately with Yes or No, but only after
mechanical devices of extreme delicacy had been carefully
appHed.

At the end of September they proclaimed their message.
It was in the affirmative, and this Yes out of far-distant tran-
scendental regions called forth a resounding echo in the world
of everyday life. Genuinely and truly the i^^ seconds of arc
had come out, correct to the decimal point. These points
representing ciphers, as it were, had chanted of the harmony
of the spheres in their Pythagorean tongue. The transmission
of this message seemed to be accompanied by the echoing
words of Goethe's " Ariel '* :

" With a crash the Light draws near !
Peahng rays and trumpet-blazes, —
Eye is blinded, ear amazes."

Never before had anything like this happened. A wave
of amazement swept over the continents. Thousands of
people who had never in their lives troubled about vibrations
of light and gravitation were seized by this wave and carried
on high, immersed in the wish for knowledge although in-
capable of grasping it. This much all understood, that from
the quiet study of a scholar an illuminating gospel for exploring
the universe had been irradiated.

During that time no name was quoted so often as that of
this man. Everything sank away in face of this universal
theme which had taken possession of humanity. The con-
verse of educated people circled about this pole, could not
escape from it, continually reverted to the same theme when

14 EINSTEIN THE SEARCHER

pressed aside by necessity or accident. Newspapers entered
on a chase for contributors who could furnish them with short
or long, technical or non-technical, notices about Einstein's
theory. In all nooks and corners social evenings of instruction
sprang up, and wandering universities appeared with errant
professors that led people out the three-dimensional misery
of daily life into the more hospitable Elysian fields of four-
dimensionality. Women lost sight of domestic worries and
discussed co-ordinate systems, the principle of simultaneity,
and negatively-charged electrons. All contemporary questions
had gained a fixed centre from which threads could be spun to
each. Relativity had become the sovereign password. In
spite of some grotesque results that followed on this state of
affairs it could not fail to be recognized that we were watching
symptoms of mental hunger not less imperative in its demands
than bodily hunger, and it was no longer to be appeased by
the former books by writers on popular science and by mis-
guided idealists.

And whilst leaders of the people, statesmen, and ministers
made vain efforts to steer in the fog, to arrive at results service-
able to the nation, the multitude found what was expedient for
it, what was uplifting, what sounded Hke the distant hammer-
ing of reconstruction. Here was a man who had stretched his
hands towards the stars ; to forget earthly pains one had but
to immerse oneself in his doctrine. It was the first time for
ages that a chord vibrated through the world invoking all eyes
towards something which, like music or religion, lay outside
political or material interests.

The mere thought that a living Copernicus was moving in
our midst elevated our feeUngs. Whoever paid him homage
had a sensation of soaring above Space and Time, and this
homage was a happy augury in an epoch so bare of brightness
as the present.

As already remarked, there was no lack of rare fruits among
the newspaper articles, and a chronicler would doubtless have
been able to make an attractive album of them. I brought
Einstein several foreign papers with large illustrations which
must certainly have cost the authors and publishers much
effort and money. Among others there were full-page beauti-

PHENOMENA IN THE HEAVENS 15

fully coloured pictures intended to give the reader an idea of
the paths pursued by the rays from the stars during the total
eclipse of the sun. These afforded Einstein much amusement,
namely, e contrario, for from the physical point of view these
pages contained utter nonsense. They showed the exact op-
posite of the actual course of the rays inasmuch as the author
of the diagrams had turned the convex side of the deflected
ray towards the sun. He had not even a vague idea of the
character of the deflection, for his rays proceeded in a straight
line through the universe until they reached the sun, where
they underwent a sudden change of direction reminiscent of a
stork's legs. The din of journaHstic homage was not unmixed
with scattered voices of dissent, even of hostility. Einstein
combated these not only without anger but with a certain
satisfaction. For indeed the series of unbroken ovations
became discomfiting, and his feeUngs took up arms against
what seemed to be developing into a star-artist cult. It was
like a breath of fresh air when some column of a chance news-
paper was devoted to a polemic against his theory, no matter
how unfounded or unreasoned it may have been, merely
because a dissonant tone broke the unceasing chorus of praise.
On one occasion he even said of a shrill disputant, *' The man
is quite right 1 '* And these words were uttered in the most
natural manner possible. One must know him personally if
one is to understand these excesses of toleration. So did
Socrates defend his opponents.

In our conversation we returned to the original question,
and I asked whether there was no means of making the deflec-
tion of the ray intelligible to an average person.

Einstein replied : "In a very superficial manner this is
certainly possible." And with a few strokes on the paper,
which I shall here try to describe in words, he gave his explana-
tion in terms something like the following :

This square is to denote the cross-section of a closed box
which we imagine to be situated somewhere in the universe.
Inside it there lives a physicist who makes observations and
draws inferences from them. In the course of time he per-
ceives, what is famiUar to all of us, that every body not sup-
ported and left to itself, for example, a stone that is released,
drops to the floor with uniform acceleration, that is, with a

16 EINSTEIN THE SEARCHER

steady increase of velocity in going downwards. There are
two ways open to him to explain this phenomenon.

Firstly, he might suspect — and this suspicion would be
most likely to occur to him — that his box was resting on some
body in the heavens. For if indeed the box were a cave in
some part of the world, the falling of the stone would suggest
nothing unusual ; it would be quite self-evident to every
occupant, and quite explicable to the physicist according to
GaUlei's (or Newton's) Laws for Falling Bodies. He need not
necessarily restrict himself to the Earth, for if the box happened
to be on some other star, this phenomenon of falling would
likewise occur, with greater or less speed, and the body would
certainly fall with uniform acceleration. Thus the physicist
could say : this is an effect of gravitation, exhibiting the pro-
perty of weight which I explain to myself as usual, as due to
the attraction of a heavenly body.

Secondly, another idea might strike him. For we stipulated
nothing about the position of the box, and assumed only that
it was to exist " somewhere in the universe." The physicist
in the box might reason as follows :

Supposing I am separted by incalculable distances from
every attracting heavenly body, and supposing gravitation
existed neither for me nor for the stone which I release from my
hand, then it would still be possible for me to give a complete
explanation of the phenomena I observe. I should only have
to assume that the body is moving with uniform acceleration
" upwards." The motion previously interpreted by me as a
falling " downwards " need not take place at all. The stone,
as an inert body, could persist in its position (relative to the
box or the observer), and would, in spite of this, show exactly
the same behaviour when the box moves with acceleration
upwards as if it were falhng with increasing velocity downwards.

Now since our physicist has no system which might serve
for reference and orientation, and since in his box which is shut
off from the universe he has no means at his disposal of deter-
mining whether he is in the sphere of influence of an attracting
heavenly body or not, both the above explanations are feasible
for him and both are equally vahd, and it is impossible for him
to come to a decision in his choice. He can interpret the
acceleration in either way, as being upwards or downwards.

PHENOMENA IN THE HEAVENS 17

connected to one another by relativity ; a fundamental reason
for preferring one interpretation to the other cannot be
furnished, since the phenomenon of falling is represented
unchanged whether he assumes the stone to be falhng and the
box to be at rest, or vice versa. This may be generahzed in
these words :

At every point of the world the observed acceleration of a
body left to itself may be interpreted either as a gravitational
or as an inertial effect — that is, from the point of view of
physics we may assert with equal right that the system (the
box, the complex defining the orientation) from which I ob-
serve the event is accelerated, or that the event takes place in
a gravitational field. The equal right to these two views is
called the " Principle of Equivalence " by Einstein. It asserts
the equivalence or the identity of inertial and gravitational
mass. If we famiHarize ourselves with this identity, an
exceedingly important road to knowledge is opened up to our
consciousness. We arrive at the inevitable conclusion that
every inertial effect that we perceive in bodies, the most
essential quahty of it, itself so to speak in its persistent nature,
is to be traced back to the influence to which it is subjected
by other bodies. When this has become clear to us, we feel
impelled to inquire how a ray of Hght would behave under the
influence of gravitation. Hence we return to our physicist in
the box, and we now know that as a consequence of the
Principle of Equivalence we are free to assume either that an
attracting heavenly body, such as the sun,is situate dsome where
below the box, or to refer the phenomena to the box regarded
as being accelerated upwards. In the box we distinguish the
floor, the ceiling, four walls, and among these again, according
to the position we take up, the wall on the left and its opposite
one on the right.

We now imagine a marksman to be outside the box and
having no connexion with us, being poised freely in space,
and suppose him to fire out of a horizontal gun at the box so
that the bullet pierces both the wall on the left and the wall
on the right. Now, if everything else were to remain at rest,
the holes in both walls would be equally distant from the
floor, and the bullet would move in a straight line parallel to
the floor and to the ceiUng. But, as we have seen, all events

18 EINSTEIN THE SEARCHER

happen as if the box itself moved with constant acceleration.
The bullet that requires time to pass from one wall to the
other thus finds that when it reaches the wall on the right
the latter has advanced a Uttle, so that the resulting hole is a
little lower than that on the left wall. This means that the
flight of the bullet, according to our observation in the interior
of the box, is no longer rectiUnear. In fact, if we trace the
bullet from point to point, we should find that for us, situated
in the box, it would describe a line bent downwards, with its
concave side to the floor.

Exactly the same thing happens with a ray of light which
is emitted by a source outside in a horizontal direction and
which traverses the space between the walls (supposed trans-
parent). Only the velocity would be different. In the course
of its flight the ray would move like a projectile that is whizzing
along at the rate of 180,000 miles per second. But pro-
vided sufiiciently deHcate means of measurement are applied,
it should still be possible to prove the existence of an in-
finitesimal deflection from the rectilinear horizontal path,
an insignificant concavity towards the floor.

Consequently this curvature of the Hght-ray (say, from a
star) must also be perceptible in places where it is subject to
the influence of a gravitational field. If we drop our imaginary
picture of the box, the argument is in nowise altered. A ray
from a star which passes close by the sun seems to our per-
ception to be bent in towards the sun, and the order of this
deflection can be determined if sufiiciently deUcate instru-
ments be used. As above remarked, it is a question of detect-
ing a difference of 1*7 seconds of arc, which is to be manifested
as a distance on the photographic plate, and is actually found
to be present.

The fact that scientists are able to detect this appears in
itself a marvel of technical precision far in advance of " split-
ting hairs," for in comparison a single hair is, in this case, to be
removed to a considerable distance if we are to use it to give
an idea of the size of angle under consideration. Fortunately
stellar photography has been developed so wonderfully that in
every single case extraordinarily accurate results are got even
from prehminary measurements.

In ordinary astronomical practice it is usually found that

PHENOMENA IN THE HEAVENS 19

a millimetre in linear measure on the plate corresponds to a
minute of arc. This means that the sun's disc itself has a
diameter of 3 centimetres on the photograph. The stars
appear as tiny dots, which may be sharply differentiated in an
enlargement. Stars of the fourteenth order of magnitude and
beyond it become visible, whereas the naked eye cannot see
those of order higher than the sixth. A grating whose lines
are tw millimetre wide is copied on to the plate to make the
measurement more accurate, so that the positions of objects
can be ascertained with certainty to within a few tenths of a
second of arc. Thus the problem which was to be solved by
the solar eclipse of 1919 lay within the realm of possibility as
regards our means of measurement.

A copy of this photograph had been sent to Einstein from
England, and he told me of it with evident pleasure. He
continually reverted to the delightful little picture of the
heavens, quite fascinated by the thing itself, without the
slightest manifestation of a personal interest in his own success.
Indeed, I may go further and am certainly not mistaken in
saying his new mechanics did not even enter his head, nor the
verification of it by the plate ; on the contrary, he displayed
that disposition of the mind which in the case of genius as well
as in that of children shows itself as naivete. The prettiness
of the photograph charmed him, and the thought that the
heavens had been drawn up as for parade to be a model for it.

All things are repeated in the history of life. In these
happenings, which mark the 29th May 1919 as a red-letter day
in the history of science, we recognize a revival of the Sun
Myth, unperceived by the individual, but as an expression of
the universal consciousness, just as when Copernicus con-
verted the geocentric picture of the universe into a helio-
centric one, the Sun Myth again sprang into life ; the sym-
bolization of faith in the light -giving and heat -giving star.
This time it has arisen, purified of all dross, scarcely perceptible
to our senses, like an aureole spun about the sun by far-distant
sources of light, in honour of a principle, and even if most of
us do not yet know what a " system of reference " means, yet
for many such a system has unconsciously evolved, a thought-
system serving as a reference for the development of their
knowledge when they thought or spoke of Einstein.

CHAPTER II
BEYOND OUR POWER

Useful and Latent Forces. — Connexion between Mass, Energy, and Velocity
of Light. — Deriving Power by Combustion. — One Gramme of Coal. — 'Un-
obtainable Calories. — Economics of Coal, — Hopes and Fears. — Dissociated
Atoms.

2(^th March 1920

WE spoke of the forces that are available for man and
which he derives from Nature as being necessary for
his existence and for the development of Hfe. What
forces are at our disposal ? What hopes have we of elaborating
our supply of these forces ?

Einstein first explained the conception of energy, which
is intimately connected with the conception of mass itself.
Every amount of substance (I am paraphrasing his words),
the greatest as well as the smallest, may be regarded as a
store of power, indeed, it is essentially identical with energy.
All that appears to our senses and our ordinary understanding
as the visible, tangible mass, as the objective body corre-
sponding to which we, in virtue of our individual bodies,
abstract the conceptual outlines, and become aware of the
existence of a definite copy is, from the physical point of
view, a complex of energies. These in part act directly, in part
exist in a latent form as strains which, for us, begin to act
only when we release them from their state of strain by some
mechanical or chemical process, that is, when we succeed in
converting the potential energy into kinetic energy. It may
be said, indeed, that we have here a physical picture of what
Kant called the " thing in itself.'' Things as they appear
in ordinary experience are composed of the sum of our direct
sensations ; each thing acts on us through its outHne, colour,
tone, pressure, impact, temperature, motion, chemical be-
haviour, whereas the thing in itself is the sum-total of its
energy, in which there is an enormous predominance of those

BEYOND OUR POWER 21

energies which remain latent and are quite inaccessible in
practice.

But this *' thing in itself," to which we shall have occasion
to refer often with a certain regard to its metaphysical sig-
nificance, may be calculated. The fact that it is possible to
calculate it takes its origin, like many other things which had
in no wise been suspected, in Einstein's Theory of Relativity.

Quite objectively and without betraying in the sHghtest
degree that an astonishing world-problem was being dis-
cussed, Einstein expressed himself thus :

" According to the Theory of Relativity there is a calcul-
able relation between mass, energy, and the velocity of Hght.
The velocity of Hght (denoted by c, as usual) is equal to
3*io^° cm. per second. Accordingly the square of c is equal
to 9 times lo^^ cm. per second, or, in round numbers, lo^i cm.
per second. This c^ plays an essential part if we introduce into
the calculation the mechanical equivalent of heat, that is,
the ratio of a certain amount of energy to the heat theoretically
derivable from it ; we get for each gramme 20*10^2^ that is,
20 billion calories.'*

We shall have to explain the meaning of this brief physical
statement in its bearing on our practical lives. It operates
with only a small array of symbols, and yet encloses a whole
universe, widening our perspective to a world-wide range !

To simplify the reasoning and make it more evident we
shall not think of the conception of substance as an inimitable
whole, but shall fix our ideas on a definite substance, say coal.

There seems little that may strike us when we set down the
words :

" One Gramme of Coal."

We shall soon see what this one gramme of coal conveys
when we translate the above-mentioned numbers into a
language to which a meaning may be attached in ordinary
life. I endeavoured to do this during the above conversa-
tion, and was grateful to Einstein for agreeing to simplify his
argument by confining his attention to the most valuable fuel
in our economic life.

Once whilst I was attending a students' meeting, paying
homage to Wilhelm Dove, the celebrated discoverer took us
aback with the following remark : When a man succeeds in

22 EINSTEIN THE SEARCHER

climbing the highest mountain of Europe he performs a task
which, judged from his personal point of view, represents
something stupendous. The physicist smiles and says quite
simply, ** Two pounds of coal." He means to say that by
burning 2 lb. of coal we gain sufficient energy to lift a man
from the sea-level to the summit of Mont Blanc.

It is assumed, of course, that an ideal machine is used,
which converts the heat of combustion without loss into work.
Such a machine does not exist, but may easily be imagined by
supposing the imperfections of machines made by human
hands to be eliminated.

Such effective heat is usually expressed in calories. A calorie
is the amount of heat that is necessary to raise the tempera-
ture of a gramme of water by one degree centigrade. Now
the theorem of the Mechanical Equivalent, which is founded
on the investigations of Camot, Robert Mayer, and Clausius,
states that from one calorie we may obtain sufficient energy
to lift a pound weight about 3 feet. Since 2 lb. of coal
may be made to yield 8 million calories, they will enable
us to lift a pound weight through 24 milUon feet, theoretically,
or, what comes to the same approximately, to lift a 17-
stone man through 100,000 feet, that is, nearly 19 miles :
this is nearly seven times the height of Mont Blanc.

At the time when Dove was lecturing, Einstein had not
yet been born, and when Einstein was working out his Theory
of Relativity, Dove had long passed away, and with him there
vanished the idea of the small value of the energy stored
in substance to give way to a very much greater value of
which we can scarce form an estimate. We should feel dumb-
founded if the new calculation were to be a matter of miUions,
but actually we are to imagine a magnification to the extent
of bilHons. This sounds almost like a fable when expressed
in words. But a milUon is related to a billion in about the
same way as a fairly wide city street to the width of the Atlantic
Ocean. Our Mont Blanc sinks to insignificance. In the above
calculation it would have to be replaced by a mountain
50 milHon miles high. Since this would lead far out into
space, we may say that the energy contained in a kilogramme
of coal is sufficient to project a man so far that he will never
return, converting him into a human comet. But for the

BEYOND OUR POWER 28

present this is only a theoretical store of energy which cannot
yet be utilized in practice.

Nevertheless, we cannot avoid it in our calculations just
as we cannot avoid that remarkable quantity c, the velocity
of Ught that plays its part in the tiny portion of substance as
it does in everything, asserting itself as a regulative factor
in all world phenomena. It is a natural constant that pre-
serves itself unchanged as 180,000 miles per second under
all conditions, and which truly represents what appeared to
Goethe as " the immovable rock in the surging sea of pheno-
mena," as a phantasm beyond the reach of investigators.

It is difficult for one who has not been soaked in all the
elements of physical thought to get an idea of what a natural
constant means ; so much the more when he feels himself
impelled to picture the constant, so to speak, as the rigid axis
of a world constructed on relativity. Everything, without
exception, is to be subjected not only to continual change (and
this was what HeracHtus assumed as a fundamental truth in
his assertion panta rhei, everything flows), but every length-
measurement and time-measurement, every motion, every
form and figure are dependent on and change with the position
of the observer, so that the last vestige of the absolute vanishes
from whatever comes into the realm of observation. Never-
theless, there is an absolute despot, who preserves his identity
inflexibly among all phenomena — the velocity of light, c, of
incalculable influence in practice and yet capable of measure-
ment. Its nature has been characterized in one of the main
propositions of Einstein stated in 1905 : *' Every ray of Hght
is propagated in a system at rest with a definite, constant
velocity independent of whether the ray is emitted by a body
at rest or in motion." But this constancy of the omnipotent
c is not only in accordance with world relativity : it is actually
the main pillar which supports the whole doctrine ; the further
one penetrates into the theory, the more clearly does one feel
that it is just this c which is responsible for the unity, con-
nectivity, and invincibility of Einstein's world system.

In our example of the coal, from which we started, c occurs
as a square, and it is as a result of multiplying 300,000 by itself
(that is, forming c^) that we arrive at the thousands of milHards
of energy units which we associated above with such a com-

24 EINSTEIN THE SEARCHER

paratively insignificant mass. Let us picture this astounding
circumstance in another way, although we shall soon see that
Einstein clips the wings of our soaring imagination. The huge
ocean liner Imperator, which can develop a greater horse-
power than could the whole of the Prussian cavalry before the
war, used to require for one day's travel the contents of two
very long series of coal-trucks (each series being as long as it
takes the strongest locomotive to pull). We now know that
there is enough energy in two pounds of coal to enable this
boat to do the whole trip from Hamburg to New York at its
maximum speed.

I quoted this fact, which, although it sounds so incredibly
fantastic, is quite true, to Einstein with the intention of justi-
fying the opinion that it contained the key to a development
which would initiate a new epoch in history and would be the
panacea of all human woe. I drew an enthusiastic picture of a
dazzHng Utopia, an orgy of hopeful dreams, but immediately
noticed that I received no support from Einstein for these
visionary aspirations. To my disappointment, indeed, I
perceived that Einstein did not even show a special interest in
this circumstance which sprang from his own theory, and which
promised such bountiful gifts. And to state the conclusion of
the story straight away I must confess that his objections were
strong enough not only to weaken my rising hopes, but to
annihilate them completely.

Einstein commenced by saying : "At present there is
not the sUghtest indication of when this energy will be ob-
tainable, or whether it will be obtainable at all. For it
would presuppose a disintegration of the atom effected at will
— a shattering of the atom. And up to the present there is
scarcely a sign that this will be possible. We observe atomic
disintegration only where Nature herself presents it, as in the
case of radium, the activity of which depends upon the con-
tinual explosive decomposition of its atom. Nevertheless, we
can only establish the presence of this process, but cannot pro-
duce it ; Science in its present state makes it appear almost
impossible that we shall ever succeed in so doing."

The fact that we are able to abstract a certain number of
calories from coal and put them to practical use comes about
owing to the circumstance that combustion is only a molecular

BEYOND OUR POWER 25

process, a change of configuration, which leaves fully intact the
atoms of which the molecules are composed. When carbon
and oxygen combine, the elementary constituent, the atom,
remains quite unimpaired. The above calculation, " mass
multipHed by the square of the velocity of light," would have
a technical significance only if we were able to attack the
interior of the atom ; and of this there seems, as remarked, not
the remotest hope.

Out of the history of technical science it might seem possible
to draw on examples contradictory to this first argument
which is soon to be followed by others equally important. As a
matter of fact, rigorous science has often declared to be impos-
sible what was later discovered to be within the reach of tech-
nical attainment — things that seem to us nowadays to be
ordinary and self-evident. Werner Siemens considered it
impossible to fly by means of machines heavier than air, and
Helmholtz proved mathematically that it was impossible.
Antecedent to the discovery of the locomotive the "impossible "
of the academicians played an important part ; Stephenson
as well as Riggenbach (the inventors of the locomotive) had
no easy task to establish their inventions in the face of the
general reproach of craziness hurled at them. The eminent
physicist Babinet applied his mathematical artillery to
demolish the ideas of the advocates of a telegraphic cable
between Europe and America. Philipp Reis, the forerunner
of the telephone, failed only as a result of the " impossible " of
the learned physicist Poggendorff ; and even when the prac-
tical telephone of Graham Bell (1876) had been found to work
in Boston, on this side of the Atlantic there was still a hubbub
of ** impossible " owing to scientific reasons. To these illustra-
tions is to be added Robert Mayer's mechanical equivalent of
heat, a determining factor in our above calculations of billions ;
it likewise had to overcome very strong opposition on the part
of leading scientists.

Let us imagine the state of mankind before the advent of
machines and before coal had been made available as a source
of power. Even at that time a far-seeing investigator would
have been able to discover from theoretical grounds the 8000
calories mentioned earlier and also their transformation into
useful forces. He would have expressed it in another way and

26 EINSTEIN THE SEARCHER

would have got different figures, but he would have arrived
at the conclusion : Here is a virtual possibility which must
unfortunately remain virtual, as we have no machine in which
it can be used. And however far-sighted he may have been,
the idea of, say, a modern dynamo or a turbine-steamer would
have been utterly inconceivable to him. He would not have
dreamed such a thing. Nay, we may even imagine a human
being of the misty dawn of prehistoric ages, of the diluvial
period, who had suddenly had a presentiment of the connexion
between a log of wood and the sun's heat, but who was yet
unaware of the uses of fire ; he would argue from his prim-
ordial logic that it was not possible and never would be possible
to derive from the piece of wood something which sends out
warmth like the sun.

I beUeve now, indeed, that we have grounds for consider-
ing ourselves able to mark off the Umits of possibihty more
clearly than the present position of science would seem to
warrant. There is the same relation between such possibilities
and absolute impossibihties as there is between Leibniz's
verttes de fait and the verites eternelles. The fact that we shall
never succeed in constructing a plane isosceles triangle with
unequal base angles is a verite eternelle. On the other hand,
it is only a verite de fait that science is precluded from giving
mortal man eternal Ufe. This is only improbable in the highest
degree, for the fact that, up to the present, all our ancestors
have died is only a finite proof. The well-known Cajus of our
logic books need not die ; the chances of his dying are only

n
—J—, where we denote the total of all persons that have passed

away up to this moment by n. If I ask a present-day
authority in biology or medicine what evidence there is that
it will be possible to preserve an individual person permanently
from death, he would confess : not the slightest. Nevertheless,
Helmholtz declared : " To a person who tells me that by using
certain means the fife of a person may be prolonged indefinitely
I can oppose my extreme disbehef, hut I cannot contradict him
absolutely."

Einstein himself once pointed out to me such very remote
possibilities ; it was in connexion with the following cir-
cumstance. It is quite impossible for a moving body ever

BEYOND OUR POWER 27

to attain a velocity greater than that of light, because it is
scientifically inconceivable. On the other hand, it is con-
ceivable, and therefore within the range of possibiUty, that
man may yet fly to the most distant constellations.

There is, therefore, no absolute contradiction to the notion
of making available for technical purposes the billions of
calories that occurred in our problem. As soon as we admit it
as possible for discussion, we find ourselves inquiring what
the solution of the problem could signify. In our intercourse
we actually arrived at this question, and discovered the most
radical answer in a dissertation which Friedrich Siemens has
written about coal in general without touching in the slightest
on these possibilities of the future. 1 imagine that this dis-
sertation was a big trump in my hand, but had soon to learn
from the reasoned contradiction of Einstein that the point
at issue was not to be decided in this way.

Nevertheless, it will repay us to consider these arguments
for a moment.

Friedrich Siemens starts from two premises which he
seemingly bases on scientific reasoning, thus claiming their
vahdity generally. They are : Coal is the measure of all
things. The price of every product represents, directly or
indirectly, the value of the coal contained in it.

As all economic values in over-populated countries are
the result of work, and as work presupposes coal, capital is
synonymous with coal. The economic value of each object
is the sum-total of the coal that had to be used to manufacture
the object in question. In over-populated states each wage
is the value of the coal that is necessary to make this extra life
possible. If there is a scarcity of coal, the wages go down in
value ; if there is no coal, the wages are of no value at all, no
matter how much paper money be issued.

As soon as agriculture requires coal (this occurs when it is
practised intensively and necessitates the use of railways,
machines, artificial manures), coal becomes involved with
food-stuffs. Thanks to industriahsm, coal is involved in
clothing and housing, too.

Since money is equivalent to coal, proper administration
of finance is equivalent to a proper administration of coal
resources, and our standard of currency is in the last

28 EINSTEIN THE SEARCHER

instance a coal-currency. Gold as money is now concen-
trated coal.

The most advanced people is that which derives from one
kilogramme of coal the greatest possibihties conducive to life.
Wise statesmanship must resolve itself into wise administra-
tion of coal. Or, as it has been expressed in other words else-
where : *' We must think in terms of coal."

These fundamental ideas were discussed, and the result
was that Einstein admitted the premises in the main, but
failed to see the conclusiveness of the inferences. He proved
to me, step by step, that Siemens' line of thought followed a
vicious circle, and, by begging the question, arrived at a false
conclusion. The essential factor, he said, is man-power, and
so it will remain ; it is this that we have to regard as the
primary factor. Just so much can be saved to advantage as
there is man-power available for purposes other than for the
production of coal from which they are now released. If we
succeed in getting greater use out of a kilogramme of coal by
better management, then this is measurable in man-power,
with which one may dispense for the mining of coal, and which
may be apphed to other purposes.

If the assertion : " Coal is the measure of all things,"
were generally valid, it should stand every test. We need
only try it in a few instances to see that the thesis does not
apply. For example, said Einstein : However much coal
we may use, and however cleverly we may dispose of it, it will
not produce cotton. Certainly the freightage of cotton-wool
could be reduced in price, but the value-factor represented by
man-power can never disappear from the price of the cotton.

The most that can be admitted is that an increase of the
amount of power obtained from coal would make it possible
for more people to exist than is possible at present, that is, that
the margin of over-population would become extended. But
we must not conclude that this would be a boon to mankind.
" A maximum is not an optimum."

He who proclaims the maximum without qualification as
the greatest measure of good is like one who studies the various
gases in the atmosphere to ascertain their good or bad effect
on our breathing, and arrives at the conclusion : the nitrogen
in the air is harmful, so we must double the proportion of

BEYOND OUR POWER 29

oxygen to counteract it ; this will confer a great benefit on
humanity 1

* Armed with this striking analogy, we can now subject
the foundation of Siemens' theory to a new scrutiny, and we
shall then discover that even the premises contain a trace of
the petitio principii that finally receives expression in the
radical and one-sided expression : " Coal is everything."

As if built on solid foundations this first statement looms
before us : Coal is solar energy. This is so far indisputable.
For all the coal deposits that are still slumbering in the earth
were once stately plants, dense woods of fern, which, bearing
the burden of milHons of years, have saved up for us what
they had once extracted as nutrition from the sun's rays. We
may let the parallel idea pass without contention : In the
beginning was not the Word, nor the Deed, but, in the be-
ginning was the Sun. The energy sent out by the sun to the
earth for mankind is the only necessary and inevitable con-
dition for deeds. Deeds mean work, and work necessitates
life. But we immediately become involved in an unjustifiable
subdivision of the idea, for the propounder of the theory says
next : "... Coal is solar energy, therefore coal is necessary
if we are to work ..." and this has already thrust us from
the paths of logic ; the prematurely victorious ergo breaks
down. For, apart from the solar energy converted into coal,
the warmth of our mother planet radiates on us, and furnishes
us with the possibility of work. Siemens' conclusion, from
the point of view of logic, is tantamount to : Graphite is solar
energy ; hence graphite is necessary, if we are to be able to
work. The true expression of the state of affairs is : Coal is,

• The parts included between * . . . • axe to be regarded as supplementary
portions intended to elucidate the arguments involved in the dialogue. In
many points they axe founded on utterances of Einstein, but also contain
reflections drawn from other sources, as well as opinions and inferences which
fall to the account of the author, as already remarked in the preface. One
will not get far by judging these statements as right or wrong, for even the
debatable view may prove itself to be expeditious and suggestive in the
perspective of these conversations. Wherever it was possible, without the
connexion being broken, I have called attention to the parts which Einstein
corrected or disapproved of. In other places I refrained from this, particu-
larly when the subject under discussion demanded an even flow of argument.
It would have disturbed the exposition if I had made mention of every
counter-argument of the opposing side in all such cases while the explanation
was proceeding along broad lines.

30 EINSTEIN THE SEARCHER

for our present conditions of life, the most important, if not the
exclusive, preUminary for human work.

And when we learn from poHtical economy that " in a
social state only the necessary human labour and the demand
for power-installations which require coal, and hence again
labour for their production, come into question," this in no
way impUes the assertion, as Siemens appears to assume, that
coal can be made out of labour. But it does signify that work
founded on the sun's energy need not necessarily be reducible
to coal. And this probably coincides with Einstein's opinion,
which is so much the more significant, as his own doctrine
points to the highest measure of effect in forces, even if only
theoretically.*

Nevertheless, it is a fact that every increase in the quantity
of power derived, when expressed per kilo, denotes a mitiga-
tion of life's burdens ; it is only a question of the limits
involved.

Firstly, is technical science with its possibilities, as far as
they can be judged at present, still able to guarantee the
future for us ? Can it spread out the effective work so far
that we may rely peacefully on the treasures of coal slumbering
in the interior of the earth ?

Evidently not. For in this case we are deahng with
quantities that may be approximately estimated. And even
if we get three times, nay ten times, as many useful calories
as before, there is a parallel calculation of evil omen that in-
forms us : there will be an end to this feast of energy.

In spite of all the embarrassments due to the present
shortage of coal we have still always been able to console
ourselves with the thought that there is really a sujSiciency,
and that it is only a question of overcoming stoppages. It is
a matter of fact that from the time of the foundation of the
German Empire to the beginning of the World War coal
production had been rising steadily, and it was possible to
calculate that in spite of the stupendous quantities that
were being removed from the black caves of Germany, there
remained at least 2000 milhards of marks in value (taken
at the nominal rate, that is, £100,000,000,000). Never-
theless, geologists and mining experts tell us that our whole
supply will not last longer than 2000 years, in the case of

BEYOND OUR POWER 81

England 500 years, and in that of France 200 years. Even
if we allow amply for the opening up of new coal-j&elds in other
continents, we cannot get over the fact that in the prehistoric
fern forests the sun has stored up only a finite, exhaustible
amount of energy, and that within a few hundred years
humanity will be faced with a coal famine.

Now, if coal were really the measure of all things, and if
the possibihty of Hfe depended only on the coal supply, then
our distant descendants would not only relapse into barbarity,
but they would have to expect the absolute zero of existence.
We should not need to worry at all about the entropy death
of the universe, as our own extinction on this earthly planet
beckons to us from an incomparably nearer point of time.

At this stage of the discussion Einstein revealed prospects
which were entirely in accordance with his conviction that the
whole argument based on the coal assumption was untenable.
He stated that it was by no means a Utopian idea that technical
science will yet discover totally new ways of setting free
forces, such as using the sun's radiation, or water power, or
the movement of the tides, or power reservoirs of Nature,
among which the present coal supply denotes only one branch.
Since the beginning of coal extraction we have lived only on
the remains of a prehistoric capital that has lain in the
treasure-chests of the earth. It is to be conjectured that the
interest on the actual capital of force will be very much in
excess of what we can fetch out of the depositories of former
ages.

To form an estimate of this actual capital, entirely in-
dependent of coal, we may present some figures. Let us
consider a tiny water canal, a mere nothing in the watery
network of the earth, the Rhine-falls at Schaffhausen, that
may appear mighty to the beholder, but only because he
applies his tourist's measure instead of a planetary one. But
even this bagatelle in the household of Nature represents very
considerable effectual values for us : 200 cubic metres spread
over a terrace 20 metres high yield 67,000 horse-power, equi-
valent to 50,000 kilowatts. This cascade alone would suffice
to keep illuminated to their full intensity 1,000,000 glow-
lamps, each of 50 candle-power, and according to our present
tariff we should have to pay at least 70,000 marks (£3500

32 EINSTEIN THE SEARCHER

nominally) per hour. The coal-worshipper will be more im-
pressed by a different calculation. The Rhine-falls at Schaff-
hausen is equivalent in value to a mine that jdelds every day
145 tons of the finest brown coal. If we took the Niagara
Falls as an illustration, these figures would have to be multi-
plied by about 80.

And by what factor would we have to multiply them, if
we wished to get only an approximate estimate of the energy
that the breathing earth rolls about in the form of the tides ?
The astronomer Bessel and the philosopher-physicist Fechner
once endeavoured to get at some comparative picture of these
events. It required 360,000 men twenty years to build the
greatest Egyptian pyramid, and yet its cubical contents are
only about the milHonth of a cubic mile, and perhaps if we sum
up everything that men and machinery have moved since
the time of the Flood till now, a cubic mile would not yet have
been completed. In contrast with this, the earth in its tidal
motion moves 200 cubic miles of water from one quadrant of
the earth's circumference to another in every quarter of a day.
From this we see at once that all the coal-mines in the world
would mean nothing to us if we could once succeed in making
even a fraction of the pulse-beat of the earth available for
purposes of industry.

If, however, we should be compelled to depend on coal,
our imaginations cling so much more closely to that enormous
quantity given by the expression mo^, which was derived from
the theory of relativity.

The 20 billion calories that are contained in each gramme
of coal exercise a fascination on our minds. And although
Einstein states that there is not the slightest indication that
we shall get at this supply, we get carried along by an irre-
sistible impulse to picture what it would mean if we should
actually succeed in tapping it. The transition from the golden
to the iron age, as pictured in Hesiod, Aratus, and Ovid, takes
shape before our eyes, and following our bent of continuing
this cyclically, we take pleasure in fancying ourselves being
rescued from the serfdom of the iron and of the coal age to a
new golden age. A supply, such as is piled up in an average
city storing-place, would be sufficient to supply the whole
world with energy for an immeasurable time. All the troubles

BEYOND OUR POWER 33

and miseries arising from the running of machines, the
mechanical production of wares, house-fires would vanish, and
all the human labour at present occupied in mining coal would
become free to cultivate the land, all railways and boats would
run almost without expense, an inconceivable wave of happi-
ness would sweep over mankind. It would mean an end of
coal-, freight-, and food-shortage ! We should at last be able
to escape out of the hardships of the day, which is broken
up by strenuous work, and soar upwards to brighter spheres
where we would be welcomed by the true values of hfe. How
alluring is the song of Sirens chanted by our physics with its
high " C," the velocity of Hght to the second power, which
we have got to know as a factor in this secret store of energy.

But these dreams are futile. For Einstein, to whom we
owe this formula so promising of wonders, not only denies
that it can be appUed practically, but also brings forward
another argument that casts us down to earth again. Sup-
posing, he explained, it were possible to set free this enormous
store of energy, then we should only arrive at an age, compared
with which the present coal age would have to be called
golden.

And, unfortunately, we find ourselves obliged to fall in
with this view, which is based in the wise old saw fJLTj^h dyav,
ne quid nimis, nothing in excess. Applied to our case, this
means that when such a measure of power is set free, it does
not serve a useful purpose, but leads to destruction. The
process of burning, which we used as an illustration, calls up
the picture of an oven in which we can imagine this wholesale
production of energy, and experience tells us that we should
not heat an oven with dynamite.

If technical developments of this kind were to come about,
the energy supply would probably not be capable of regulation
at all. It makes no difference if we say that we only want
a part of those 20 bilUon calories, and that we should be glad
to be able to multiply the 8000 calories required to-day by
100. That is not possible, for if we should succeed in disin-
tegrating the atom, it seems that we should have the billions
of calories rushing unchecked on us, and we should find our-
selves unable to cope with them, nay, perhaps even the solid
ground, on which we move, could not withstand them.

3 I

34 EINSTEIN THE SEARCHER

No discovery remains a monopoly of only a few people.
If a very careful scientist should really succeed in producing
a practical heating or driving effect from the atom, then any
untrained person would be able to blow up a whole town
by means of only a minute quantity of substance. And any
suicidal maniac who hated his fellows and wished to pulverize
all habitations within a wide range would only have to con-
ceive the plan to carry it out at a moment's notice. All the
bombardments that have taken place ever since fire-arms
were invented would be mere child's play compared with the
destruction that could be caused by two buckets of coal.

At intervals we see stars light up in the heavens, and
then become extinguished again ; from these we infer that
world catastrophes have occurred. We do not know whether
it is due to the explosion of hydrogen with other gases, or to
collisions between two stellar bodies. There is still room for
the assumption that, immeasurably far away in yonder regions
of celestial space, something is happening which a malevolent
inhabitant of our earth, who has discovered the secret of
smashing the atom, might here repeat. And even if our
imaginations can be stretched to paint the blessings of this
release of energy, they certainly fail to conjure up visions
of the disastrous effects which would result.

Einstein turned to a page in a learned work of the mathe-
matical physicist Weyl of Ziirich, and pointed out a part that
dealt with such an appalling liberation of energy. It seemed
to me to be of the nature of a fervent prayer that Heaven
preserve us from such explosive forces ever being let loose
on mankind !

Subject to present impossibility, it is possible to weave
many parallel instances. It is conceivable that by some yet
undiscovered process alcohol may be prepared as plentifully
and as cheaply as ordinary water. This would end the short-
age of alcohol, and would assure dehrium tremens for hundreds
of thousands. The evil would far outweigh the good, although
it might be avoidable, for one can, even if with great difficulty,
imagine precautionary measures.

War technique might lead to the use of weapons of great
range, which would enable a small number of adventurers to
conquer a Great PQW^r, It will be objected : this will hold

BEYOND OUR POWER 35

vice versa, too. Nevertheless, this would not alter the fact
that such long-range weapons would probably lead to the
destruction of civiHzation. Our last hope of an escape would
be in a superior moral outlook of future generations, which
the optimist may imagine to himself as the force majeure.

There are apparently only two inventions, in themselves
triumphs of intellect, against which one would have no defence.
The first would be thought-reading made applicable to all,
and with which Kant has dealt under the term " thinking
aloud." What is nowadays a rare and very imperfect tele-
pathic " turn '* may yet be generalized and perfected in a
manner which Kant supposed not impossible on some distant
planet. The association and converse of man with his fellows
would not stand the test of this invention, and we should have
to be angels to survive it even for a day.

The second invention would be the solution of this mc^-
problem, which I call a problem only because I fail to discover
a proper term, whereas so far was it from being a problem
for Einstein that it was only in my presence he began to
reckon it out in figures from the symboHc formula. To
us average beings a Utopia may disclose itself, a short
frenzy of joy followed by a cold douche : Einstein stands
above it as the pure searcher, who is interested only in the
scientific fact, and who, even at the first knowledge of it,
preserves its essentially theoretical importance from attempts
to apply it practically. If, then, another wishes to hammer
out into a fantastic gold-leaf what he has produced as a
httle particle of gold in his physical investigations, he offers
no opposition to such thought-experiments, for one of the
deepest traits of his nature is tolerance.

A. Pfliiger, one of the best qualified heralds of the
new doctrine, has touched on the above matter in his
essay, The Principle of Relativity. Einstein praised this
pamphlet ; I mentioned that the author took a view differ-
ent from that of Einstein, of the possibiHty of making ac-
cessible the wc2. In discussing the practical significance of
this eventuaHty, Pfliiger says : "It will be time to talk of
this point again a hundred years hence.'* This seems a
short time-limit, even if none of us will Uve to be present at
the discussion. Einstein smiled at this pause of a hundred

36 EINSTEIN THE SEARCHER

years, and merely repeated, " A very good essay ! '* It is
not for me to offer contradictions ; and, as far as the implied
prognostication is concerned, it will be best for mankind
if it should prove to be false. If the optimum is unattainable,
at least we shall be spared the worst, which is what the reahza-
tion of this prophecy would inflict on us.

Some months after the above discussion had first been
put to paper, the world was confronted by a new scientific
event. The EngUsh physicist Rutherford had, with deliberate
intention, actually succeeded in spHtting up the atom.
When I questioned Einstein on the possible consequences of
this experimental achievement, he declared with his usual
frankness, one of the treasures of his character, that he had
now occasion to modify somewhat the opinion he had shortly
before expressed. This is not to mean that he now considered
the practical goal of getting unUmited supply of energy as
having been brought within the realm of possibility. He gave
it as his view that we are now entering on a new stage of
development, which may perhaps disclose fresh openings for
technical science. The scientific importance of these new
experiments with the atom was certainly to be considered very
great.

In Rutherford's operations the atom is treated as if he
were dealing with a fortress : he subjects it to a bombardment
and then seeks to fire into the breach. The fortress is still
certainly far from capitulating, but signs of disruption have
become observable. A hail of bullets caused holes, tears,
and spHnterings.

The projectiles hurled by Rutherford are alpha-particles
shot out by radium, and their velocity approaches two-thirds
that of light. Owing to the extreme violence of the impact,
they succeeded in doing damage to certain atoms enclosed in
evacuated glass tubes. It was shown that atoms of nitrogen
had been disrupted. It is still unknown what quantities of
energy are released in this process. This spUtting up of the
atom carried out with intention can, indeed, be detected only
by the most careful investigations.

As far as practical appHcations are concerned, then, we
have got no further, although we have renewed grounds for
hope. The unit of measure, as it were, is still out of pro-

BEYOND OUR POWER 87

portion to the material to be cut. For the forces which
Rutherford had to use to attain this result are relatively very
considerable. He derived them from a gramme of radium,
which is able to Uberate several milUard calories, whereas the
net practical result in Rutherford's experiment is still im-
measurably small. Nevertheless, it is scientifically estabUshed
that it is possible to spUt up atoms of one's own free will,
and thus the fundamental objection raised above falls to
the ground.

There is also another reason for increased hope. It seems
feasible that, under certain conditions, Nature would auto-
matically continue the disruption of the atom, after a human
being had intentionally started it, as in the analogous case of
a conflagration which extends, although it may have started
from a mere spark.

A by-product of future research might lead to the trans-
mutation of lead into gold. The possibiHty of this transforma-
tion of elements is subject to the same arguments as those
above about the spHtting up of the atom and the release of
great quantities of energy. The path of decay from radium
to lead Ues clearly exposed even now, but it is very question-
able whether mankind will finally have cause to offer up hymns
of thanksgiving if this line from lead on to the precious metals
should be continued, for it would cause our conception of the
latter to be shattered. Gold made from lead would not give
rise to an increase in the value of the meaner metal, but to the
utter depreciation of gold, and hence the loss of the standard
of value that has been valid since the beginning of our civiliza-
tion. No economist would be possessed of a sufficiently
far-sighted vision to be able to measure the consequences on
the world's market of such a revolution in values.

The chief product would, of course, be the gain in energy,
and we must bear this in mind when we give ourselves up to
our speculations, however optimistic or catastrophic they may
be. The impenetrable barrier " impossible " no longer exists.
Einstein's wonderful *' Open Sesame," mass times the square
of the velocity of light, is thundering at the portals.

And mankind finds a new meaning in the old saw : One
should never say never !

CHAPTER III
VALHALLA

Order of Distinction and Chaxacteri^tics \oi\ Great Discoverers. — Galilei
and Newton. — Forerunners and Priority. — Science and Religion. — Inherit-
ance of Talent. — A Dynasty of Scholars. — Alexander von Humboldt and
Goethe. — Leonardo da Vinci. — Helmholtz. — Robert Mayer and Diihring. —
Gauss and Riemann. — Max Planck. — Maxwell and Faraday.

I HAD made up my mind to question Einstein about a
number of famous men, not concerning mere facts of
their lives and works, for these details were also pro-
curable elsewhere, and, moreover, I was not ignorant of them,
but what attracted me particularly was to try to discover how
the greatness of one might be compared with that of another.
This sometimes helps us to see a personahty in a different Hght
and from a new perspective, which leads us to assign to him a
new position in the series of orders of merit.

I had really sketched out a list for this purpose, including
a great number of glorious names from the annals of physics
and regions just beyond : a table, as it were, from which one
might set up a directory for Valhalla ! It seemed to me a
pleasing thought to roam through this hall of celebrities in
company with Einstein, and to pause at the pedestal of the
busts of the great, who, in spite of their number, are still too
few, far too few, in comparison with the far too many who
populate the earth Hke so many factory-produced articles.
If we set to work to draw up a Ust of this sort, we soon find
that there is no end to these heroes of Valhalla, and we are
reminded of the hall of fame of the Northern Saga, of the
mythological Valhalla, whose ceiUng was so high that the
gable was invisible, and whose extent was so great that any-
one wishing to enter could choose from five hundred and forty
entrances.

In reahty our Httle excursion was far from taking these
dimensions, the chief reason being probably that we had

38

VALHALLA 89

begun at Newton. However attractive it may be to hear
Einstein talk of Newton, a disadvantage arises in that we
find it hard to take leave of his bust situated at the main
portal, and that we continually revert to it even when we
call to mind the remaining paths free for our choice and
stretching out of sight.

Reality, even figuratively, offered a picture which differed
considerably from the measures of greatness apportioned
by legendary accounts. In Einstein's workroom, certainly,
a visitor encounters portraits, not busts, and it would be rash
to speak of this little collection of portraits as of a miniature
museum. No, it is certainly not that, for its catalogue num-
bers only to three. But here they act as a trinity with a
special significance under the gaze of Einstein, who looks up
to them with reverence. To him their contribution of thought
is immeasurable ; Faraday, Maxwell with his rich coils of
hair, and between them, Newton with his flowing wig, repre-
sented in an excellent English engraving, whose border con-
sists of symbolic insignias encircling his distinguished-looking
countenance.

According to Schopenhauer, the measure of reverence that
one can feel is a measure of one's own intrinsic value. Tell
me how much respect you can feel, and I shall tell you w^hat
is your worth. It is certainly not necessary to emphasize
this quality specially in the case of Einstein, for there are other
points of vantage from which we may form an estimate of
his excellence. Nevertheless, I make special mention of the
circumstance to give an indication of the difference between a
revolutionary discoverer and revolutionary pioneers in other
fields. It is particularly noticeable that inborn respect is
seldom found in modernists of Art. The only means of pro-
paganda known to them consists in a passionate denunciation
of what has been developed historically by gradual and patient
effort ; their retrospect consists of unmitigated contempt ;
they profess to be disciples only of what is most recent, re-
maining confined within the narrow circle surrounding their
own ego. The horizon of the discoverer has a different radius.
He takes over responsibiUty for the future by never ceasing his
offerings at the altar of the Past. There is probably no dis-

40 EINSTEIN THE SEARCHER

coverer who is devoid of this characteristic, but I should Hke
to emphasize that, among all the scientists with whom I am
acquainted, no one recognizes the merit of others so warmly
as Einstein. He becomes carried away with enthusiasm when
he talks of great men, or of such as appear great to him. His
Valhalla is not, of course, the same as that favoured by Ency-
clopaedias, and many a one whom we rank as a Sirius among
men is to be found lower than the sixth order of magnitude
in Einstein's list. Nevertheless, the number of selection of
constellations is no mean one, and the reverence that was
originally inspired by reasoned thought has become infused
in his temperament and become a part of his emotional self.

One need only mention the name of Newton — and even
this is scarcely necessary, for Newton seems always near at
hand ; if I happen to start with Descartes or Pascal, it does
not take long before we arrive at Newton. dpSpa ^ol eweirr) !

Once we began with Laplace ; and it seemed almost as if the
*' Trait e de la mechanique celeste " was to become the subject
of discussion. But Einstein left his seat, and, taking up a
position in front of his series of portraits on the wall, he medi-
tatively passed his hand through his hair, and declared :

" In my opinion the greatest creative geniuses are Gahlei
and Newton, whom I regard in a certain sense as forming a
unity. And in this unity Newton is he who has achieved
the most imposing feat in the realm of science. These two
were the first to create a system of mechanics founded on a
few laws and giving a general theory of motions, the totality
of which represents the events of our world."

Interrupting his remarks, I asked : " Can GaUlei's funda-
mental law of inertia (Newton's First Law of Motion) be
said to be a law deduced from experience ? My reason for
asking is that the whole of natural science is a science of ex-
perience, and not merely something based on speculation.
It might easily suggest itself to one that an elementary law
like that of Galilei or Newton could be derived from our every-
day experience. But, if this is the case, how is it that science
had to wait so long before this simple fact was discovered ?
Experience is as old as the hills ; why did the law of inertia
not make its appearance at the very beginning, when Nature
was first subjected to inquiry ? "

VALHALLA 41

'* By no means ! " replied Einstein. *' The discovery of
the law of rectihnear motion of a body under no external
influences is not at all a result of experience. On the contrary !
A circle, too, is a simple line of motion, and has often been
proclaimed as such by predecessors of Newton, for example,
by Aristoteles. It required the enormous power of abstrac-
tion possessed only by a giant of reason to stabilize rectilinear
motion as the fundamental form."

To this may be added that before and even after the time
of Galilei, not only the circle but also other non-rectiUnear lines
have been regarded even by serious thinkers as the primary
hues given by Nature ; these thinkers even dared to apply
their curvilinear views to explaining world phenomena that
could be made clear only after Galilei's abstraction had been
accepted.

I asked whether the theory of gravitation was already
impHcitly contained in GaHlei's Laws of FalKng Bodies. Ein-
stein's answer was in the negative : the gravitational theory
falls entirely to the credit of Newton, and the greatness of this
intellectual achievement remains unimpaired even if the efforts
of certain forerunners are recognized. He mentioned Robert
Hooke, whom, among others, Schopenhauer sets up against
Newton, with absolute injustice and from petty feelings of
antipathy, which takes its origin from Schopenhauer's un-
mathematical type of mind. The vast difference between
Hooke's preKminary attempts at explaining gravitation, and
Newton's monumental structure, was beyond his power of
discernment.

* Schopenhauer (vol. ii. of the Par ergo) uses two arguments
to discredit Newton. Firstly, he refers to two original works,
both of which he misinterprets ; secondly, he undertakes a
psychological analysis of Newton. He uses psychological
means, which would be about equally reasonable as applying
the Integral Calculus to proving facts of Ethical Psychology,
and he arrives at the conclusion that priority in discovering
the law of gravitation is due to some one else ; Hooke is pictured
as having been treated like Columbus : we now hear of
" America," and likewise " Newton's Gravitational System " !

Schopenhauer has, however, quite forgotten that he him-
self, some pages earlier, trumpeted forth Newton's imperishable

42 EINSTEIN THE SEARCHER

fame with the words : "To form an estimate of the great
value of the gravitational system which was at least completed
and firmly established by Newton, we must remind ourselves
how entirely nonplussed about the origin of the motion of
celestial bodies thinkers had previously been for thousands of
years." That bears the ring of truth. Newton's greatness
can be grasped only if thousands of years are used as a measure.
Whereas Schopenhauer argued from grounds drawn from
psychology and the principle of universal knowledge, his anta-
gonist Hegel, who was still more vague in these fields, sought to
dispense with both Newton and Kepler by calling to his aid
the so-called pure intuition of the curved line. In an exposition
of truly comical prolixity, such as would have deUghted the
hearts of schoHasts, he proves that the elhpse must represent
the fundamental type of planetary motion, this being quite in-
dependent of Newton's laws, Kepler's observations, and result-
ing mathematical relationships. And Hegel actually succeeds,
with a nebulous verbosity almost stultifying in its unmeaning-
ness, in paraphrasing Kepler's second law in his own fashion.
It reads Uke an extract from some carnival pubUcation issued
by scientists in a bibulous mood to make fun of themselves.

But these extravagances, too, serve to add lustre to Newton,
for his genius shines out most brilHantly when it is a question of
expressing clearly, and without assumptions, a phenomenon of
cosmic motion. Here there are no forerunners, not even with
regard to his own law of gravitation. Newton showed with
truly triumphant logic that Kepler's second law belongs to
those things that are really self-evident.

This law, taken alone, offers considerable difficulties to
anyone who learns of it for the first time. Every planet
describes an ellipse ; that is accepted without demur. But the
uninitiated will possibly or even probably deduce from this
that the planet will pass over equal lengths of arc in equal
times. By no means, says Kepler ; the arcs traversed in equal
times are unequal. But if we connect every point of the
elliptic path with a definite point within the curve (the focus
of the ellipse) by means of straight lines, each of which is called
a radius vector, we get that the areas swept out by the radius
vector in equal times (and not the arcs) are equally great.
Why is this so ? This cannot be understood a priori. But

VALHALLA 48

one might argue that since the attraction of the sun is the
governing force, this will probably have something to do with
Newton's law of gravitation, in particular with the inverse
square of the distance. And one might further infer that, if
a different principle of gravitation existed, Kepler's law would
assume a new form.

A fact amazing in its simpUcity here comes to Ught.
Newton states the proposition : " According to whatever
law an accelerating force acts from a centre on a body moving
freely, the radius vector will always sweep out equal areas in
equal lengths of time."

Nothing is assumed except the law of inertia and a Httle
elementary mathematics, namely, the theorem that triangles
on the same base and of the same altitude are equal in area.
The form in which this theorem occurs in Newton's simple
drawing is certainly astonishing. One feels that there in a
few strokes a cosmic problem is solved ; the impression is
ineffaceable.

This theorem together with its proof is contained in
Newton's chief work, Philosophice naturalis principia mathe-
matica. The interfusion of philosophy and mathematics
furnished him with the natural principles of knowledge.*

Einstein made some illuminating remarks about Newton's
famous phrase : " Hypotheses non fingo." I had said that
Newton must have been aware that it is impossible to build
up a science entirely free from hypotheses. Even geometry
itself has arrived at that critical stage at which Gauss and
Riemann discovered its hypothetical foundations.

Einstein rephed : " Accentuate the words correctly and
the true sense will reveal itself ! " It is the last word that is
to be stressed and not the first. Newton did not want to feel
himself free from hypotheses, but rather from the assumption
that he invented them, except when this was absolutely
necessary. Newton, then, wished to express that he did not
go further back in his analysis of causes than was absolutely
inevitable.

Perhaps, I allowed myself to interject, a more violent
suspicion against the word " hypotheses " was prevalent with
scholars in Newton's time than now. Newton's emphatic
defence would then appear a shade more inteUigible Or did

44 EINSTEIN THE SEARCHER

he cherish the belief that his world-law was the only possible
one in Nature ?

Einstein again referred to the universahty of Newton's
genius, saying that Newton was doubtless aware of the
range within which his law was vaHd : this law appHes to the
realm of observation and experience, but is not given a priori,
no more than Galilei's Law of Inertia. It is certainly con-
ceivable that beyond the domain of human experience there
may be an undiscoverable universe in which a different funda-
mental law holds, and one which, nevertheless, does not contra-
dict the principle of sufficient reason.

The antithesis : SimpHcity — Complexity, led the conversa-
tion into a short bypath ; it arose out of an example which
I quoted and that I shall repeat here even if it may seem
irrelevant.

One might well expect that just as for attraction there
must be a general law for resistance or repulsion. And if
attraction occurs according to the inverse square of the
distance, then it would be an extremely interesting parallel if
a similar law were to hold for repulsion except that the pro-
portionaUty were direct instead of inverse. There have
actually been physicists who have proclaimed a direct square
law of repulsion ; I have heard it in lectures myself. The
action of a resisting medium, as, for example, the resistance of
the air to the flight of a cannon-ball, is stated to be proportional
to the square of the velocity of the projectile.

This theorem is wrong. If it were correct, and verified by
experiment, we should have to regard it as being presumably
the only possible and directly evident form of the law of re-
pulsion or resistance. There would, at least, be no logical
reason for contradicting it.

But here we have a mixed relationship, as Einstein calls it —
that is, we are unable to express an exact connexion between
the velocity of a body in flight and the air resistance.

This fallacious assumption by no means proceeded from
illogical reasoning, and it seemed to rest on a sound physical
basis. For, so it was argued, if the velocity is doubled, there
is twice as much air to be displaced, so that the resistance will
be four times as great. But this was contradicted outright by
experimental evidence. One cannot even call it an approxi-

VALHALLA 45

mate law, except for very low speeds. For greater speeds
we find, instead of a quadratic relation, a cubical one, or one
of a more complex nature. Photographs have demonstrated
that the resistance experienced by a projectile in flight is due
to the excitation of a powerful central wave, to the friction
between the air and the surface of the projectile, and to eddies
produced behind the projectile — that is, to various conjoined
factors, each of which follows a different law, and such that
the combined effect cannot be expressed by a simple formula
at all. This phenomenon is thus very complicated and offers
almost insuperable difficulties to analysis. A beautiful
remark was once made, which characterizes such events in
Nature.

During a conversation with Laplace, Fresnel said that
Nature does not worry about analytical difficulties. There
is nothing simpler than Newton's Law in spite of the
complicated nature of planetary motions. " Nature here
despises our analytical difficulties," said Fresnel ; " she applies
simple means, and then by combining them produces an almost
inextricable net of confusion. Simplicity lies concealed in
this chaos, and it is only for us to discover it ! " But this
simplicity when it is discovered is not always found to be
expressible in simple formulae, not must it be forgotten that
even the ultimate discoverable simplicity points to certain
hypothetical assumptions.

" Hypotheses non fingo ! " This phrase of Newton's
remains true, if we maintain Einstein's interpretation : " He
did not wish to go further back in his analysis of causes than
was absolutely inevitable." It interested me to pursue this
line of thought suggested by Einstein still further, and I
discovered that these words of Newton had actually been
falsely accentuated and hence misinterpreted by many
authorities on science. Even Mill and the great scholar,
William Whewell, succumbed to this misunderstanding.
Credit must be given to a more modem scholar. Professor
Vaihinger of Halle, for being sufficiently keen of hearing to
detect the true accentuation ; and now that Einstein has
corroborated fully this explanation, doubts as to the true
sense of the words are no longer to be feared.

The trend of our talk brought us to a discussion of the

40 EINSTEIN THE SEARCHER

conception, "law of nature.*' Einstein recalled Mach's
remarks, and indicated that the point was to determine how
much we read out of Nature ; and these observations made at
least one thing clear, namely, that every law signifies some
limitation ; in the case of human laws, expressed in the civil
and penal code, the Umitation affects the will, and possible
actions, whereas natural laws signify the Umitations which we,
taught by experience, prescribe to our expectations. Never-
theless, the conception remains elastic, for the question will
always intrude itself : What does prescription mean ? Who
prescribes ? Kant has assigned to Man the foremost position
inasmuch as it is he who is regarded by Kant as prescribing
laws to Nature. Bacon of Verulam emphasizes the ambiguous
point of view by asserting : " Natura non vincitur nisi parendo,"
Man conquers Nature only by obeying her, that is, by conform-
ing to her immanent norms. Thus the laws exist without
us, and we have only to discover them. When they have been
found, Man can react by applying them to subdue Nature.
Man becomes the dictator and dictates to Nature the laws
according to which she for her part has to subjugate mankind.
Whether we adopt the one view or the other, there is a vicious
circle, from which there is no escape. A law is a creation of
intellect, and Mephisto's words remain true : " In the end we
depend on the creatures of our own making ! "

In Newton's soul obedience and the wish to obey must
have been pre-eminent traits. Is he not reputed to have
been pious and strong of faith ?

Einstein confirmed this, and, raising his voice, he generalized
from it, saying : "In every true searcher of Nature there is a
kind of religious reverence ; for he finds it impossible to
imagine that he is the first to have thought out the exceedingly
deHcate threads that connect his perceptions. The aspect
of knowledge which has not yet been laid bare gives the in-
vestigator a feeUng akin to that experienced by a child who
seeks to grasp the masterly way in which elders manipulate
things."

This explanation implied a personal confession. For he
had spoken of the childhke longing felt by all, and had inter-
preted the subtle intricacies of the scientist's ideas in par-
ticular as springing from a religious source. Not all have

VALHALLA 47

confessed this ; we know, indeed, that the convictions of
many a one were not so. Let us cling to the fact that the
greatest in the realm of science — Newton, Descartes, Gauss,
and Helmholtz — were pious, although their faith varied in
degree. And let us not forget that the most bitter opponent
of this attitude of mind, the originator of " Ecrasez I'infame,"
finally had a temple built bearing the inscription : ** Deo
erexit Voltaire."

In Newton positivism found its most faithful disciple, and
his research was directly affected by his religious attitude. He,
himself, was the author of that beautiful thought : '* A limited
measure of knowledge takes us away from God ; an increased
measure of knowledge takes us back to Him." It was he who
considered that the world-machine that he had disclosed was
not sufficiently stabiUzed by his mathematical law, and so he
enlisted the intermittent help of an assistant for the Creator,
Concursus Dei, to attend to the functioning of the machine.
Finally, he slipped from the path of naive faith on to theo-
logical bypaths and wrote devout essays on apocalyptic matters.
On the other hand, Descartes' piety, which was genuine at root,
exhibited suspicious offshoots, and one cannot shake off the
feeling that he was smiling up his sleeve when he was making
some of his solemn declarations. He was a master of com-
promise, and gave due expression to its spirit, which F. A.
Lange bluntly stated was merely a veil for " Cowardice
towards the Church." Voltaire, an apostle of Newton's
system of natural philosophy, went so far in his condemnation
of Descartes' confession of faith that he affirmed: "The
Cartesian doctrine has been mainly instrumental in persuading
many not to recognize a God."

As Einstein had called special attention to the childlike
nature of the scientist's root-impulse, I quoted a remark of
Newton that seemed to me at the moment to be a confirma-
tion of Einstein's attitude :

'* I do not know what I may appear to the world, but
to myself I seem to have been only like a boy playing on
the seashore, and diverting myself in now and then find-
ing a smoother pebble or a prettier shell than ordinary,
whilst the great ocean of truth lay all undiscovered before
me.

48 EINSTEIN THE SEARCHER

Are we not to regard this analogy of Newton's as being
intended to convey a religious meaning ?

" There is no objection to this/' said Einstein, " although
it seems to me more probable that, in saying this, Newton set
down the view only of the pure investigator. The essential
purpose of his remarks was to express how small is the range
of the attainable compared with the infinite expanse offered
for research."

Through some unexpected phrase that was dropped, the
conversation took a new turn at this point, which I should
not Hke to withhold, inasmuch as it gave rise to a noteworthy
observation of Einstein about the nature of genius. We were
talking about the "possibiUty of genius for science being
inherited " and about the comparative rareness with which
it occurs. There seems to have been only one case of a real
dynasty of great minds, that of the ten Bernoullis who were
descended of a line of mathematicians, and all of them achieved
important results, some of them making extraordinary dis-
coveries. Why is this exception unique ? In other examples
we do not get beyond three or four names in the same family,
even if we take Science and Art conjointly. There were two
Plinys, two GaHleis, two Herschels, two Humboldts, two
Lippis, two Dumas, several Bachs, Pisanos, Robbias, and
Holbeins — the net result is very poor, even if we count similar
names, disregarding the fact of relationship ; there is no
recognizable dynasty except in the case of the ten Bernoullis.*
" And so," I continued, " the conclusion seems justified that
Nature has nothing to do with a genealogy of talents, and
that, if we happen to notice manifestations of talent in one
and the same family, this is a mere play of chance."

Einstein, however, contradicted this emphatically : " In-
herited talent certainly occurs in many cases, where we do not
observe it, for genius in itself and the possibihty of genius
being apprehended are certainly far from always appearing in
conjunction. There are only insignificant differences between
the genius that expresses itself in remarkable achievements and

* The Roman family Cosmati (of the thirteenth century) , which gave us
seven splendid representatives of architecture and mosaic work, hardly comes
into consideration, since not one of themj^is regarded in the history of art as
a real genius.

VALHALLA 49

the genius that is latent. At a certain instant, perhaps, only
some impulse was wanting for the latent genius to burst forth
with all clearness and brilhance ; or, perhaps, it required only
an unusual situation in the development of science to call
into action his special talents, and thus it remained dormant,
whereas a very sHght change of circumstances would have
caused them to assert themselves in definite results.

" In passing I should Uke to remark that you just now
mentioned the two Humboldts ; it seems to me that Alexander
von Humboldt, at least, is not to be counted as a genius. It
has struck me repeatedly that you pronounced his name with
particular reverence "

" And I have observed equally often, Professor, that you
made a sign of disapproval. For this reason sHght doubts
have gradually been rising in me. But it is difficult to get free
from the orders of greatness that one has recognized for de-
cades. In my youth people spoke of ' a Humboldt * just
as we speak of ' a Caesar ' or ' a Michelangelo,' to denote
some pinnacle of unrivalled height. To me at that time
Humboldt's Kosmos was the Bible of Natural Science, and
probably such memories have a certain after-effect."

" That is easy to understand," said Einstein. " But we
must make it clear to ourselves that for us of the present day
Humboldt scarcely comes into consideration when we direct
our gaze on to the great seers. Or, let us say more clearly,
he does not belong to this category. I certainly grant him
his immense knowledge and his admirable faculty of getting
into touch with the unity of Nature, which reminds us of
Goethe."

" Yes ; this feeling for the uniformity of the cosmos had
probably persuaded me in his favour," I answered, " and I am
glad that you draw a parallel with Goethe in this respect. It
reminds me of Heine's story : If God had created the whole
world, except the trees and the birds, and had said to Goethe :
' My dear Goethe, I leave it to you to complete this work,'
Goethe would have solved the problem correctly and in a god-
like manner — that is, he would have painted the trees green
and given the birds feathers.

" Humboldt could equally well have been entrusted with
this task. But various objections may be raised against such
4

50 EINSTEIN THE SEARCHER

reflections of a playful poetic character . . . one objection
being that Goethe's own knowledge of ornithology was ex-
ceedingly limited. Even when nearly eighty he could not
distinguish a lark from a yellow-hammer or a sparrow ! Is
that a fact ? "

'* Fully confirmed : Eckermann gives a detailed report of
it in a conversation which took place in 1827. As I happened
to come across the passage only yesterday, I can quote the
exact words if you will allow me : * Great and good man,'
thought Eckermann, ' who hast explored Nature as few have
ever done, in ornithology thou seemest still a child ! * "

For a speculative philosopher, it may here be interposed,
this might well serve as the starting-point of an attractive
investigation. Goethe, on the one hand, cannot recognize a
lark, but would have been able to grasp the Platonic idea
of the feathered species, even if there had been no such things
as birds : Humboldt, on the other hand, would perhaps have
been able to create the revolving planets, if Heaven had com-
manded it ; but he would never have succeeded in becoming
the author of what we call an astronomical achievement,,
such as that of Copernicus or of Kepler.

And with reference to certain other men I elicited from
Einstein utterances that reduced somewhat my estimate of
their importance.

We were speaking of Leonardo da Vinci, omitting all
reference to his significance in the world of Art — that is, only
of Leonardo the Scholar and the Searcher. Einstein is far
from disputing his place in the Valhalla of great minds, but
it was clear that he wished to recommend a re-numbering of
my Hst, so that the Italian master would not occupy a position
in just the first rank.

The problem of Leonardo excited great interest in me,
and it deserves the consideration of every one. The further
the examination of his writings advances, the more does this
problem resolve itself into the question : How much altogether
does modern science owe to Leonardo ? Nowadays it is
declared in all earnestness that he was a painter and a sculptor
only by the way, that his chief profession was that of an
engineer, and that he was the greatest engineer of all times.
This has in turn given rise to the opinion that, as a scientist.

VALHALLA 51

he is the Hght of all ages, and in the abundance of his dis-
coveries he has never been surpassed before or after his own
time.

As this question had arisen once before, I had come
equipped with a little table of facts, hastily drawn from special
works to which I had access. According to my scheme,
Leonardo was the true discoverer and author of the following
things :

Law of Conservation of Momentum.

Law of Virtual Velocities (before Ubaldi and Galilei).

Wave Theory (before Newton).

Discovery of the Circulation of the Blood (before

Harvey).
Laws of Friction (before Coulomb).
Law of Pressure for connected Tubes containing

Fluid (before Pascal).
Action of Pressure on Fluids (before Stevin and GaUlei).
Laws of Falling Bodies (before Galilei).
True interpretation of the twinkling of stars (before
Kepler, who, moreover, did not succeed in finding
the real explanation).
Explanation of the reflected light of the moon (before

Kepler).
Principle of Least Action (before GaHlei).
Introduction of the plus and the minus signs into

calculations.
Definition of kinetic energy from mass and velocity.
Theory of Combustion (before Bacon).
Explanation of the motion of the sea (before Maury).
Explanation of the ascent of fluids in plants (before

Hales).
Theory of Fossilization (before Palissy).
Added to these there are a great number of inventions,
in particular those connected with problems of aviation, such
as the parachute (before Lenormand), and so forth.

This list aroused great distrust in Einstein : he regarded
it as the outcome of an inquisitive search for sources, excusable
historically, but leading to misrepresentation. We are falsely
led to regard sfightly related beginnings, vague tracks, hazy
indications, which are found, as evidences of a real insight.

52 EINSTEIN THE SEARCHER

which disposes us to ** elevate one above all others." Hence
a mythological process results, comparable to that which, in
former times, thrust all conceivable feats of strength on to
one Hercules.

I learned that recently a strong reaction has asserted
itself in scientific circles against this one-sided hero-worship ;
its purpose is to reduce Leonardo's merits to their proper
measure. Einstein made it quite clear that he was certainly
not to be found on the side of the vQtra-Leonardists.

It cannot be denied that the latter have valuable arguments
to support their case, and that these arguments become
multipUed in proportion as the pubhcation of Leonardo's
writings (in the Codex Atlanticus, etc.), which are so difficult to
decipher, proceeds. The partisans of Leonardo derive consider-
able support in many points from recognized authorities, as
in the case of Cantor, the author of the monumental history
of mathematics. We there read : " The greatest ItaUan
painter of the fifteenth century was not less great as a scientist.
In the history of science his name is famous and his achieve-
ments are extolled, particularly those which give him a claim
to be regarded as one of the founders of Optics." He is
placed on a level with Regiomantus as one of the chief builders
of mathematics of that time. Nevertheless, Cantor raises
certain doubts by remarking that the results of investigations
made up to the present do not prove Leonardo to be a great
mathematician. On another page he is proclaimed simultane-
ously with Archimedes and Pappus as a pioneer of the doctrines
of the centre of gravity.

With regard to the main points, Leonardo's priority in
the case of the Laws of Falling Bodies, the Theory of Wave-
motion, and the other fundamental principles of physics,
Einstein has the conviction that the partisans of Leonardo
are either mistaken in the facts or that they overlook fore-
runners. In the case of these principles, above all, there is
always some predecessor, and it is almost impossible to trace
the Une of discoveries back to the first source. Just as writers
have wished to deprive Galilei, Kepler, and Newton of their
laurels in favour of Leonardo, so the same might be done with
Copernicus.

This has actually been attempted. The real Copernicus,

VALHALLA 53

so one reads, was Hipparchus of Nicsea, and if we go back
still further, a hundred years earlier, two thousand years ago,
we find that Aristarchus of Samos taught that the world
rotated about its own axis and revolved round the sun.

And we need not even stop there, in Einstein's opinion.
For it is open to conjecture that Aristarchus in his turn has
drawn on Egyptian sources. This retrogressive investigation
may excite the interest of archaeologists, and in particular
cases perhaps lead to the discovery of a primary claim to
authorship, but it cannot fail to excite suspicion against the
conscious intention of conferring all the honours of science
on an individual discoverer. Leonardo's superlative con-
structive genius is not attacked in these remarks, and there
seems no reason for objecting if anyone wishes to call him
the most ingenious engineer of all times.

All the pressures and tensions occurring in Nature seemed
to be repeated in him as ** inner virtues," an expression
borrowed from Helmholtz, who used it with reference to
himself. This analogy might be extended by saying that,
in the works of both, Man himself with his organic functions
and requirements plays an important role. For them the
abstract was a means of arriving at what was perceptual,
physiologically useful, and stimulating in its effect on life.
Leonardo started out from Art, and throughout the realm
of mechanics and machines he remained an artist in method.
Helmholtz set out from the medical side of physiology and
transferred the valuations of beauty derived from the senses
to his pictures of mechanical relationships. The life-work
of each has an aesthetic colouring, Leonardo's being of a
gloomy hue, that of Helmholtz exhibiting brighter and happier
tints. Common to both is an almost inconceivable versatility
and an inexhaustible productivity.

Whenever Einstein talks of Helmholtz he begins in warm
terms of appreciation, which tend to become cooler in the
course of the conversation. I cannot quote his exact words,
and as I cannot thus give a complete account for which full
responsibility may be taken, it may be allowable to offer a
few important fragments that I have gathered.

Judged by the average of his accompUshments, Helmholtz
is regarded by Einstein as an imposing figure whose fame in

54 EINSTEIN THE SEARCHER

later times is assured ; Helmholtz himself tasted of this im-
mortality while still alive. But when efforts are made to rank
him with great thinkers of the cahbre of Newton, Einstein
considers that this estimate cannot be fully borne out. In
spite of all the excellence, subtlety, and effectiveness of Helm-
holt z's astoundingly varied inspirations, Einstein seems to fail
to discover in him the source of a really great intellectual
achievement.

At a Science Congress held in Paris in 1867, at which Helm-
holtz was present, a colleague of his was greeted with unanimous
applause when he toasted him with the words : " L'ophthal-
mologie etait dans les tenebres, — Dieu parla, que Helmholtz
naquit — Et la lumiere etait faite ! " It was an almost exact
paraphrase of the homage which Pope once addressed to
Newton. At that time the words of the toast were re-echoed
throughout the world ; ophthalmology was enlarged to science
generally, and the apotheosis was applied universally. Du
Bois-Reymond declared that no other nation had in its scientific
Uterature a book that could be compared with Helmholtz's
works on Physiological Optics and on Sensations of Tone.
Helmholtz was regarded as a god, and there are not a few to
whom he still appears crowned with this divine halo.

A shrill voice pierced the serene atmosphere, attacking one
of his main achievements. The dissentient was Eugen Duhring,
to whose essay on the Principles of Mechanics a coveted
prize was awarded, a fact which seemed to stamp him as being
specially authorized to be a judge of pre-eminent achievements
in this sphere. Diihring's aim was to dislodge one of the funda-
mental supports of Helmholtz's reputation by attacking his
" Law of the Conservation of Energy." If this assault
proved successful, the god would lie shattered at his own
pedestal.

Diihring, indeed, used every means to bespatter his fair
name in science ; and it is hardly necessary to remark that
Einstein abhors this kind of polemic. What is more, he re-
gards it as a pathological symptom, and has only a smile of
disdain for many of Diihring's pithy sa5ings. He regards
them as documents of unconscious humour to be preserved
in the archives of science as warnings against future repetitions
of such methods.

VALHALLA 55

Diihring belonged also to those who wished to exalt one
above all others. He raised an altar to Robert Mayer, and
offered up sanguinary sacrifices. Accustomed to doing his
work thoroughly, he did not stop at Helmholtz in choosing
his victims. No hecatomb seemed to him too great to do
honour to the discoverer of the Mechanical Equivalent of
Heat, and so his next prey was Gauss and Riemann.

Gauss and Riemann ! Eachwas a giant in Einstein's opinion.
He knew well that this raging Ajax had also made an assault
against them, but he had no longer a clear recollection of the
detailed circumstances ; as the references were near at hand,
he allowed me to repeat a few lines of this tragi-comedy.

Helmholtz, according to Diihring (who also calls him
" Helmklotz "), has done no more than distort Mayer's funda-
mental mechanical idea, and interpret it falsely. By " philo-
sophizing " over it, he has completely spoilt it, and rendered
it absurd. It was the greatest of all humiliations practised
on Mayer that his name had been coupled with that of one
whom he had easily out-distanced, and whose clumsy attempts
at being a physicist were even worse than those by which he
sought to establish himself as a philosopher.

The offences of Gauss and Riemann against Mayer are
shrouded in darkness. But there was another would-be
scientist, Justus von Liebig, who, being opposed to Mayer,
aroused the suspicions of Diihring, particularly as he had used
his " brazen-tongue " to defend the two renowned mathe-
maticians. After he, and Clausius too, had been brought to
earth, Diihring launched out against the giants of Gottingen.
In the chapter on Gauss and " Gauss- worship," we read :
*' His megalomania rendered it impossible for him to take
exception to any tricks that the deficient parts of his own
brain played on him, particularly in the realm of geometry.
Thus he arrived at a pretentiously mystical denial of Euclid's
axioms and theorems, and proceeded to set up the founda-
tions of an apocalyptic geometry not only of nonsense but of
absolute stupidity. . . . They are abortive products of the
^eranged mind of a mathematical professor, whose mxania for
greatness proclaims them as new and superhuman truths ! . . .
The mathematical delusions and deranged ideas in question
are the fruits of a veritable paranoia geometrica.'*

56 EINSTEIN THE SEARCHER

After Herostratus had burnt to ashes the consecrated
temple, the Ionian cities issued a proclamation that his name
was to be condemned to perpetual oblivion ! The iconoclast
Diihring is immortalized, for, apart from the charge of arson,
he is notable in himself. In his case we found ourselves con-
fronted with unfathomable problems of a scholar's complex
nature, problems which even a searcher like Einstein failed to
solve. The simplest solution would be to turn the tables and
to apply the term " paranoia ** as a criticism to the book on
Robert Mayer, and thus demolish it. But this will not do,
for if we merely pass over the pages of distorted thought,
we are still left with a considerable quantity of valuable
material.

Does Diihring, after all, himself deserve a place in our
Valhalla ? The question seems monstrous, and yet cannot
be directly answered in the negative. The individual is to
be judged according to his greatest achievement, and not
according to his aberrations. The works of Aristotle teem
with nonsensical utterances, and Leonardo's Bestiarius is an
orgy of abstruse concoctions. If Diihring had written nothing
beyond his studies of personalities ranging from Archimedes
to Lagrange, the portals would yet have been open to him.
Even in his eulogy of Robert Mayer, which is besmirched
with unseemly remarks, he displays at least the courage of his
convictions.

The attempt at a comparison between Robert Mayer and
Helmholtz is doomed to failure even when considered dis-
passionately, inasmuch as the disturbing factor of priority here
intrudes itself. The definite fixing of the Law of Energy is
certainly to the credit of Helmholtz, but perhaps he would have
gained by lajdng more stress on the discovery of it five years
earlier by the doctor in Heilbronn. And again, this would
not have been final, for the invariance of the sum of energy
during mechanical actions was known even by Huyghens.
The Heilbronn doctor performed one act of genius in his life,
whereas Helmholtz during his whole Hfe moved asymptotically
to the Une of genius without ever reaching it. If my inter-
pretation of Einstein's opinion is correct, Helmholtz is to be
credited with having the splendour of an overpowering gift
for research predominant in his nature, but is not necessarily

VALHALLA 57

to be given a seat among the most illustrious of his branch of
science. Einstein wishes to preserve a certain line of demarca-
tion between this type and not only the Titans of the past,
but also those of the present. When he speaks of the latter,
his tone becomes warmer. He does not need circuitous
expressions, each syllable rings with praise. He has in
mind, above all, Hendrik Antoon Lorentz in Leyden, Max
Planck, and Niels Bohr ; we then see that he feels Valhalla
about him.

The reason that I have tried to maintain the metaphor of
a Temple of Fame is due to an echo of Einstein's own words
at a celebration held in honour of the sixtieth birthday of
the physicist Planck in the May of 1918. This speech created
the impression of a happy harmony resulting from a fusion
of two melodies, one springing from the intellect, the other
rising from the heart. We were standing as at the Propylons
with a new Heraclitus uttering the cry : Introite, nam et hie
dii sunt !

I should hke to give the gist of this beautiful address in
an extract uninterrupted by commentaries.

" The Temple of Science " — so Einstein began — " is a
complex structure of many parts. Not only are the inmates
diverse in nature, but so also are the inner forces that they
have introduced into the temple. Many a one among them
is engaged in Science with a happy feeling of a superior mind,
and finds Science the sport which is congenial to him, and
which is to give him an outlet for his strong life-forces, and to
bring him the realization of his ambitions. There are, indeed,
many, too, who offer up their sacrifice of brain-matter only
in the cause of useful achievements. If now an angel of heaven
were to come and expel all from the temple who belonged to
these two categories, a considerable reduction would result,
but there would still remain within the temple men of present
and former times : among these we count our Planck, and
that is why he has our warm affection.

' ' I know full well that, in doing this, we have light-heartedly
caused many to be driven out who contributed much to the
building of the temple ; in many cases our angel would find
a decision difficult. . . . But let us fix our gaze on those

58 EINSTEIN THE SEARCHER

who find full favour with him ! Most of them are peculiar,
reserved, and lonely men, who, in spite of what they have
in common, are really less alike than those who have been
expelled. What led them into the temple ? . . . In the first
place, I agree with Schopenhauer that one of the most powerful
motives that attract people to Science and Art is the longing
to escape from everyday life with its painful coarseness and
unconsoling barrenness, and to break the fetters of their own
ever-changing desires. It drives those of keener sensibility
out of their personal existence into the world of objective
perception and understanding. This motive force is similar
to the longing which makes the city-dweller leave his noisy,
confused surroundings and draws him with irresistible force to
restful Alpine heights, where his gaze covers the wide expanse
lying peacefully before him on all sides, and softly passes
over the motionless outlines that seem created for all eternity.
Associated with this negative motive is a positive one, by
virtue of which Man seeks to form a simplified s5moptical
view of the world in a manner conformable to his own nature,
in order to overcome the world of experience by replacing it,
to a certain degree, by this picture. This is what the painter
does, as also the poet, the speculative philosopher, and the
research scientist, each in his own way. He transfers the
centre of his emotional existence into this picture, in order
to find a sure haven of peace, one such as is not offered in the
narrow limits of turbulent personal experience.

" What position does the world-picture of the theoretical
physicist occupy among all those that are possible ? He
demands the greatest rigour and accuracy in his representation,
such as can be gained only by using the language of mathe-
matics. But for this very reason the physicist has to be more
modest than others in his choice of material, and must confine
himself to the simplest events of the empirical world, since
all the more complex events cannot be traced by the human
mind with that refined exactness and logical sequence which
the physicist demands. ... Is the result of such a restricted
effort worthy of the proud name * world-picture ' ?

" I believe this distinction is well deserved, for the most
general laws on which the system of jdeas set upjby theoretical
physics is founded claim to be valid for every kind of natural

VALHALLA 59

phenomenon. From them it should be possible by means of
pure deduction to find the picture, that is, the theory, of every
natural process, including those of hving organism, provided
that this process of deduction does not exceed the powers
of human thought. Thus there is no fundamental reason
why the physical picture of the world should fall short of
perfection. . . .

" Evolution has shown that among all conceivable theor-
etical constructions there is at each period one which shows
itself to be superior to all others, and that the world of
perception determines in practice the theoretical system,
although there is no logical road from perception to the
axioms of the theory, but rather that we are led towards
the latter by our intuition, which establishes contact with
experience. . . .

' ' The longing to discover the pre-established harmony recog-
nized by Leibniz is the source of the inexhaustible patience
with which we see Planck devoting himself to the general
problems of our science, refusing to allow himself to be dis-
tracted by more grateful and more easily attainable objects. . . .
The emotional condition which fits him for his task is akin
to that of a devotee or a lover ; his daily striving is not the
result of a definite purpose or a programme of action, but
of a direct need. . . . May his love for Science grace his
future course of life, and lead him to a solution of that all-
important problem of the day which he himself propounded,
and to an understanding of which he has contributed so
much ! May he succeed in combining the Quantum Theory
with Electrodynamics and Mechanics in a logically complete
system ! "

" What grips me most in your address," I said, " is that
it simultaneously surveys the whole horizon of science in
every direction, and traces back the longing for knowledge
to its root in emotion. When your speech was concluded,
I regretted only one thing — that it had ended so soon.
Fortunate is he who may study the text."

" Do you attach any importance to it ? " asked Einstein ;
" then accept this manuscript." It is due to this act of
generosity that I have been able to adorn the foregoing de-

60 EINSTEIN THE SEARCHER

scription of the excursion into Valhalla with such a valuable
supplement.

The conversation had begun with the briUiant constella-
tion Galilei-Newton, and near the end inclined again towards
the consideration of a double-star : the names of Faraday
and Maxwell presented themselves.

" Both pairs," Einstein declared, " are of the same magni-
tude. I regard them as fundamentally equal in their services
in the onward march of knowledge."

'* Should we not have to add Heinrich Hertz as a third
in this bond ? This assistant of Helmholtz is surely regarded
as one of the founders of the Electromagnetic Theory of Light,
and we often hear their names coupled, as in the case of the
Maxwell- Hertz equations."

" Doubtless," repUed Einstein, " Hertz, who is often
mentioned together with Maxwell, has an important rank
and must be placed very high in the world of experimental
physics, yet, as regards the influence of his scientific personahty,
he cannot be classed with the others we have named. Let
us, then, confine ourselves to the twin geniuses Faraday and
Maxwell, whose intellectual achievement may be summarized
in a few words. Classical mechanics referred all phenomena,
electrical as well as mechanical, to the direct action of particles
on one another, irrespective of their distances from one
another. The simplest law of this kind is Newton's expres-
sion : ' Attraction equals Mass times Mass divided by the
square of the distance.' In contradistinction to this, Faraday
and Maxwell have introduced an entirely new kind of physical
reaUties, nsivnely, fields of force. The introduction of these new
reaUties gives us the enormous advantage that, in the first
place, the conception of action at a distance, which is contrary
to our everyday experience, is made unnecessary, inasmuch
as the fields are superimposed in space from point to point
without a break ; in the second place, the laws for the field,
especially in the case of electricity, assume a much simpler
form than if no field be assumed, and only masses and motions
be regarded as realities."

He enlarged still further on the subject of fields, and
while he was describing the technical details, I saw him

VALHALLA 61

metaphorically enveloped in a magnetic field of force. Here,
too, an influence, transmitted through space from point to
point, made itself felt, and there could be no question of
action " at a distance " inasmuch as the effective source was
so near at hand. His gaze, as if drawn magnetically, passed
along the wall of the room and fixed affectionately on Maxwell
and Faraday.

CHAPTER IV
EDUCATION

School Curricula and Reform of Teaching. — Value of Language Study.
— Economy of Time. — Practice in Manual Work. — Picturesque Illustrations.
— Art of Lecturing. — Selection of Talents by Means of Examinations. —
Women Students. — Social Difficulties. — Necessity as Instructress.

OUR conversation turned towards a series of paedagogic
questions, in which Einstein is deeply interested.
For he himself is actively engaged in teaching, and
never disguises the pleasure which he derives from imparting
instruction. Without doubt he has a gift of making his spoken
words react on wide circles anxious to be instructed, composed
not only of University students, but of many others quite outside
this category. When, recently, popular lectures on a large
scale were instituted, he was one of the first to ofier his services
in this sound undertaking. He lectured to people of the
working class, who could not be assumed to have any pre-
liminary information on the subject, and he succeeded in
presenting his lectures so that even the less trained minds could
easily follow his argument.

His attitude towards general questions of school education
is, of course, conditioned by his own personality and his own
work in the past. His first care is that a young person should
get an insight into the relationship underl5dng natural pheno-
mena, that is, that the curricula should be mapped out so that
a knowledge of facts is the predominating aim.

'* My wish," Einstein declared to me, " is far removed from
the desire to eliminate altogether the fundamental features of
the old grammar schools, with their preference for Latin, by
making over-hasty reforms, but I am just as Httle incHned
to wax enthusiastic about the so-called humanistic schools.
Certain recollections of my own school life suffice to prevent
this, and still more, a certain presentiment of the educational
problems of the future." — " To speak quite candidly," he

EDUCATION 63

said, " in my opinion the educative value of languages is, in
general, much over-estimated."

I took the liberty of quoting a saying that is still regarded as
irrefutable by certain scholars. It was Charles V who said :
" Each additional acquired language represents an additional
personality " ; and to suggest the root of language formation he
said it in Latin : " Quot linguas quis callet, tot homines valet."
This saying has been handed down through the ages in German
in the form : *' Soviel Sprachen, soviel Sinnen " (An added
language means an added sense).

Einstein replied : "I doubt whether this aphorism is
generally vahd, for I beheve that it would at no time have
stood a real test. All experience contradicts it. Otherwise
we should be compelled to assign the highest positions among
intellectual beings to hnguistic athletes like Mithridates,
Mezzofanti, and similar persons. The exact opposite, indeed,
may be proved, namely, that in the case of the strongest per-
sonalities, and of those who have contributed most to pro-
gress, the multipHcity of their senses in no wise depended on a
comprehensive knowledge of languages, but rather that they
avoided burdening their minds with things that made excessive
claims on their memories."

" Certainly," said I, "it may be admitted that this gives
rise to exaggeration in some cases, and that the hnguistic sort
of sport practised by many a scholar degenerates to a mere
display of knowledge. An intellectual achievement of lasting
merit has very rarely or never been the result of a super-
abundance of acquired Hnguistic knowledge. An instance
occurs to me at this moment. Nietzsche became a philosopher
of far-reaching influence only after he had passed the stage of
the philologist. As far as our present discussion is concerned,
the question is narrowed down considerably : it reduces itself
to inquiring whether we do sufficient, too Uttle, or too much
Greek and Latin. I must remark at the very outset that,
formerly, school requirements went much further in this
respect than nowadays, when we scarcely meet with a scholar
even in the upper classes who knows Latin and Greek perfectly."

It is just this fact that Einstein regards as a sign of im-
provement and a result of examining the true aims of a school.
He continued : " Man must be educated to ' react dehcately ' ;

64 EINSTEIN THE SEARCHER

he is to acquire and develop * intellectual muscles * ! And
the methods of language drill are much less suited to this pur-
pose than those of a more general training that gives greatest
weight to a sharpening of one's own powers of reflection.
Naturally, the incUnation of the pupil for a particular profession
must not be neglected, especially in view of the circumstance
that such i^iclination usually asserts itself at an early age,
being occasioned by personal gifts, by examples of other
members of the family, and by various circumstances that affect
the choice of his future Hfe-work. That is why I support the
introduction into schools, particularly schools devoted to
classics, of a division into two branches at, say, the fourth
form, so that at this stage the young pupil has to decide in
favour of one or other of the courses. The elementary founda-
tion to the fourth form may be made uniform for all, as they are
concerned with factors on education that are scarcely open to
the danger of being exaggerated in any one direction. If
the pupil finds that he has a special interest in what are
called humaniora by the educationist, let him by all means
continue along the road of Latin and Greek, and, indeed, with-
out being burdened by tasks that, owing to his disposition,
oppress or alarm him."

** You are referring," I interposed, " to the distress which
pupils feel in the time allotted to mathematics. There
are actually people of considerable intelligence who seem to be
smitten with absolute stupidity when confronted with mathe-
matics, and whose school-Ufe becomes poisoned owing to the
torment caused by this subject. There are many cases of
living surgeons, lawyers, historians, and litterateurs, who, till
late in life, are visited by dreams of their earlier mathematical
ordeals. Their horror has a very real foundation, for, whereas
the pupil who is bad at Latin yet manages to get an idea of
the language, and he who is weak in history has at least a notion
of what is being discussed, the one who is unmathematical by
nature has to worry liis way through numberless lessons in
a subject which is entirely incomprehensible to him, as if
belonging to another world and being presented to him in a
totally strange tongue. He is expected to answer questions,
the sense of which he cannot even guess, and to solve problems,
every word and every figure of which glares at him like a

EDUCATION 65

sphinx of evil omen. Sitting on each side of him are pupils
to whom this is merely play, and some of whom could complete
the whole of school mathematics within a few months at express
rate. This leads to a contrast between the pupils, which may
press with tragical force on the unfortunate member throughout
his whole school existence. That is why a reform is to be
welcomed that sifts out in time those who should be separated
from the rest, and which adapts the school curriculum as closely
as possible to individual talents."

Einstein called my attention to the fact that this division
had already been made in many schools in foreign countries, as
in France and in Denmark, although not so exclusively as
suggested by him. " Moreover," he added, " I am by no
means decided whether the torments that you mentioned are
founded primarily on absence of talent in the pupil. I feel
much more inclined to throw the responsibihty in most cases
on the absence of talent in the teacher. Most teachers waste
their time by asking questions which are intended to discover
what a pupil does not know, whereas the true art of question-
ing has for its purpose to discover what the pupil knows or
is capable of knowing. Whenever sins of this sort are com-
mitted— and they occur in all branches of knowledge — the
personaUty of the teacher is mostly at fault. The results of
the class furnish an index for the quality of the preceptor.
All things being taken into consideration, the average of
abiUty in the class moves, with only slight fluctuations,
about mean values, with which tolerably satisfactory results
may be obtained. If the progress of the class is not up to
this standard, we must not speak of a bad year but rather
of an inefficient instructor. It may be assumed that, as a
rule, the teacher understands the subject with which he is
entrusted, and has mastered its content, but not that he
knows how to impart his information in an interesting manner.
This is almost always the source of the trouble. If the teacher
generates an atmosphere of boredom, the progress is stunted
in the suffocating surroundings. To know how to teach is to
be able to make the subject of instruction interesting, to
present it, even if it happens to be abstract, so that the soul
of the pupil resonates in sympathy with that of his instructor,
and so that the curiosity of the pupil is never allowed to wane.'*
5

66 EINSTEIN THE SEARCHER

" That is in itself an ideal postulate. If we assume it to
be fulfilled, how do you wish to see the subjects distributed in
the curriculum ? *'

" We must leave the detailed discussion of this question
for another occasion. One of the main points would be the
economy of time ; all that is superfluous, vexatious, and only
intended r..s a drill must be dropped. At present the aim of
the whole course is the leaving certificate. This test must be
given up ! "

" Is that serious. Professor ? Do you wish to do away
with the examination for matriculation ? "

" Exactly. For it is Hke some fearful monster guarding
our exit from school, throwing its shadow far ahead, and
compelUng teacher and pupil to work incessantly towards
an artificial show of knowledge. This examination has been
elevated by forcible means to a level which the violently
drilled candidates can keep only for a few hours, and is then
lost to sight for ever. If it is eliminated, it will carry away
with it this painful drilling of the memory ; it will no longer
be necessary to hammer in for years what will be entirely for-
gotten within a few months, and what deserves to be for-
gotten. Let us return to Nature, which upholds the principle
of getting the maximum amount of effect from the minimum
of effort, whereas the matriculation test does exactly the
opposite."

'* Yes, but who is then to be allowed to enter the uni-
versity ? "

" Every one who has shown himself to be capable not only
in a crucial test of an accidental kind, but in his whole be-
haviour. The teacher will be the judge of this, and if he does
not know who is quahfied, he again is to be blamed. He will
find it so much the easier to decide who is sufi5ciently advanced
to obtain a leaving certificate, in proportion as the curriculum
has weighed less on the minds of the young people. Six hours
a day should be ample — ^four at school and two for home-work ;
that should be the maximum. If this should appear too little
to you, I must ask you to bear in mind that a young mind is
being subjected to strain even in leisure hours, as it has to
receive a whole world of perceptions. And if you ask how the
steadily increasing curriculum is to be covered in this very

EDUCATION 67

moderate number of hours, my answer is : Throw all that is
unnecessary overboard ! I count as unnecessary the major
part of the subject that is called * Universal History,' and
which is, as a rule, nothing more than a blurred mass of history
compressed into dry tables of names and dates. This subject
should be brought within the narrowest possible Hmits, and
should be presented only in broad outhne, without dates having
to be crammed. Leave as many gaps as you like, especially
in ancient history ; they will not make themselves felt in our
ordinary existences. In nowise can I regard it as a mis-
fortune if the pupil learns nothing of Alexander the Great, and
of the dozens of other conquerors whose documentary remains
burden his memory like so much useless ballast. If he is to
get a glimpse of the grey dawn of time, let him be spared from
Cyrus, Artaxerxes, and Vercingetorix, but rather tell him
something of the pioneers of civilization, Archimedes, Ptolemy,
Hero, Appolonius, and of inventors and discoverers, so that
the course does not resolve into a series of adventures and
massacres."

" Would it not be expedient," I Interrupted, " to take
some of the history time to branch off into an elementary
treatment of the real evolution of the state, including sociology
and the legal code ? "

Einstein does not consider this desirable, although he him-
self is deeply interested in all manifestations of public Ufe.
He does not favour an elementary political training received
at school, presumably above all owing to the fact that in this
branch the instruction cannot be removed from official in-
fluences, and because political questions require the attention
of a mature mind. His picture of how a youth is to meet the
requirements of modern Hfe is something quite different, far
removed from all theories. His whole efforts are directed at
finding a means of counteracting the tendency to overburden
one side of the youthful mind. " I should demand the intro-
duction of compulsory practical work. Every pupil must
learn some handicraft. He should be able to choose for him-
self which it is to be, but I should allow no one to grow up
without having gained some technique, either as a joiner,
bookbinder, locksmith, or member of any other trade, and
without having delivered some useful product of his trade."

68 EINSTEIN THE SEARCHER

*' Do you attach greater importance to the technique itself
or to the feeUng of social relationship with the broad masses of
the people which it engenders ? "

" Both factors are equally important to me/' said Einstein,
'* and others become added to these which help to justify my
wish in this respect. The handiwork need not be used as a
means of earning money by the pupil of the secondary school,
but it will enlarge and make more soHd the foundation on
which he will rest as an ethical being. In the first place, the
school is not to produce future officials, scholars, lecturers,
barristers, and authors, but human beings, not merely mental
machines. Prometheus did not begin his education of man-
kind with astronomy, but by teaching the properties of fire
and its practical uses. ..."

" This brings to my mind another analogy," I continued,
** namely, that of the old Meister singer, who were, all of them,
expert smiths, tinkers, or shoemakers, and yet succeeded in
building a bridge to the arts. And at bottom, the sciences,
too, belong to the category of free arts. Yet, a difficulty seems
to me to arise. In demanding a compulsory handicraft, you
lay stress on practical use, whereas in your other remarks you
declared science in itself as being utterly independent of
practice."

" I do this," replied Einstein, " only when I speak of the
ultimate aims of pure research, that is, of aims that are visible
to only a vanishing minority. It would be a complete mis-
conception of Ufe to uphold this point of view and to expect
its regulative effectiveness in cases in which we are deahng
only with the preUminaries of science. On the contrary, I
maintain that science can be taught much more practically
at schools than it is at present when bookwork has the upper
hand. For example, to return to the question of mathematical
teaching : it seems to me to be almost universally at fault, if
only for the reason that it is not built up on what is practically
interesting, what appeals directly to the senses, and what can
be seized intuitively. Child-minds are fed with definitions
instead of being presented with what they can grasp, and they
are expected to be able to understand purely conceptual things,
although they have had no opportunity given them of arriving
at the abstract by way of concrete things. It is very easy to

EDUCATION 69

do the latter. The first beginnings should not be taught in the
schoolroom at all, but in open Nature. A boy should be shown
how a meadow is measured and compared with another. His
attention must be directed to the height of a tower, to the
length of his shadow at various times, to the corresponding
altitude of the sun ; by this means he will grasp the mathe-
matical relationships much more rapidly, more surely, and
with greater zeal, than if words and chalk-marks are used to
instil into him the conceptions of dimensions, of angles, or
perchance of some trigonometrical function. What is the
actual origin of such branches of science ? They are derived
from practice, as, for example, when Thales first measured the
height of the pyramids with the help of a short rod, which he
set up at the ultimate point of the pyramid's shadow. Place
a stick in the boy's hand and lead him on to make experiments
with it by way of a game, and if he is not quite devoid of sense,
he will discover the thing for himself. It will please him to have
discovered the height of the tower without having cUmbed it,
and this is the first thrill of the pleasure which he feels later
when he learns the geometry of similar triangles and the
proportionality of their sides."

** In the matter of physics," pursued Einstein, " the first
lessons should contain nothing but what is experimental and
interesting to see. A pretty experiment is in itself often more
valuable than twenty formulae extracted from our minds ; it is
particularly important that a young mind that has yet to find
its way about in the world of phenomena should be spared from
formulae altogether. In his physics they play exactly the
same weird and fearful part as the figures of dates in Universal
History. If the experimenter is ingenious and expert, this
subject may be begun as early as in the middle forms, and one
may then count on a responsiveness that is rarely observable
during the hours of exercise in Latin grammar."

** This leads me," said Einstein, " to speak in this con-
nexion of a means of education that has so far been used only
by way of trial in class-teaching, but from an improved appUca-
tion of which I expect fruitful results later. I mean the
school cinema. The triumphal march of the cinematograph
will be continued into pedagogic regions, and here it will have
a chance to make good its wrongs in thousands of picture shows

70 EINSTEIN THE SEARCHER

in showing absurd, immoral, and melodramatic subjects. By
means of the school-film, supplemented by a simple apparatus
for projection, it would be possible firstly to infuse into certain
subjects, such as geography, which is at present wound off
organ-like in the form of dead descriptions, the pulsating fife
of a metropolis. And the fines on a map will gain an entirely
new complexion in the eyes of the pupil, if he learns, as if during
a voyage, what they actually include, and what is to be read
between them. An abundance of information is imparted by
the film, too, if it gives an accelerated or retarded view of such
things as a plant growing, an animal's heart beating, or the
wing of an insect moving. The cinema seems to me to have a
still more important function in giving pupils an insight into
the most important branches of technical industry, a know-
ledge of which should become common property. Very few
hours would suffice to impress permanently on the schoolboy's
mind how a power-station, a locomotive, a newspaper, a book,
or a coloured illustration is produced, or what takes place in
an electrical plant, a glass factory, or a gasworks. And, to
return to natural science, many of the rather difficult experi-
ments that cannot be shown by means of school apparatus
may be shown with almost as great clearness on a film. Taken
all in all, the redeeming word in school-teaching is, for me :
an increased appeal to the senses. Wherever it is possible,
learning must become living, and this principle will predominate
in future reforms of school-teaching."

University study was only touched on Hghtly during this
talk. It has become known that Einstein is a very strong
supporter of the principle of free learning, and that he would
prefer to dispense entirely with the regular documents of ad-
mission which quafify holders to attend lecture courses. This
is to be interpreted as meaning that as soon as anyone desirous
of furthering his studies has demonstrated his fitness to follow
the lecturer's reasoning by showing his abiUty in class exercises
or in the laboratory, he should be admitted immediately.
Einstein would not demand the usual certificate of " general
education," but only of fitness for the special subject, par-
ticularly as, in his own experience, he has frequently found
the cleverest people and those with the most definite aims to

EDUCATION 71

be prone to one-sidedness. According to this, even the inter-
mediate schools should be authorized to bestow a certificate
of fitness to enter on a course in a single definite subject as
soon as the pupil has proved himself to have the necessary
abihty. If he earher spoke in favour of abohshing the matricu-
lation examination, this is only an indication of his effort to
burst open the portals of higher education for every one.
Nevertheless, I remarked that, in the course of imi versify work
itself, he is not in favour of giving up all regulation concerning
the ability of the student — at least, not in the case of those who
intend to devote themselves to instruction later. He does not
desire an intermediate examination (in the nature of the
tentamen physicum of doctors), but he considers it profitable
for the future schoolmaster to have an opportunity early in
his course to prove his fitness for teaching. In this matter,
too, Einstein reveals his affectionate interest in the younger
generation, whose development is threatened by nothing so
much as by incapable teachers : the sum of these considera-
tions is that the pupil is examined as Httle as possible, but
the teacher so much the more closely. A candidate for the
teaching profession, who in the early stages of his academic
career fails to show his fitness, his individual facuUas docendi,
should be removed from the university.

There can be no doubt but that Einstein has a claim to
be heard as an authority on these questions. There are few
in the realm of the learned in whose faces it is so clearly
manifest that they are called to excite a desire for knowledge
by means of the living word, and to satisfy this desire. If
great audiences assemble around him, if so many foreign
academies open their arms to him to make him their own,
these are not only signs of a magnetic influence that emanates
from the famous discoverer, but they are indications that he
is far famed as a teacher with a captivating personality.
Let us consider what this signifies in his profession. Philo-
sophers, historians, lawyers, doctors, and theologians have at
their disposal innumerable words which they merely need to
pronounce to get into immediate contact with their audiences.
In Einstein's profession, theoretical physics, man disappears ;
it leaves no scope for the play of emotion ; its implement
mathematics — and what an instrument it is ! — bristles with

72 EINSTEIN THE SEARCHER

formal difficulties, which can be overcome only by means of
symbols and by using a language which has no means of
displa5dng eloquence, being devoid of expression, emotion,
and regular periods. Yet here we have a physicist, a mathe-
matician, whose first word throws a charm over a great crowd
of people, and who extracts from their minds, so to speak,
what, in reality, he alone works out before them. He does
not adhere closely to written pages, nor to a scheme which
has been prepared beforehand in all its details ; he develops
his subject freely, without the shghtest attempt at rhetoric,
but with an effect which comes of itself when the audience
feels itself swept along by the current. He does not need
to deUver his words passionately, as his passion for teaching
is so manifest. Even in regions of thought in which usually
only formula, like glaciers, give an indication of the height,
he discovers similes and illustrations with a human appeal,
by the aid of which he helps many a one to conquer the
mountain sickness of mathematics. His lectures betray two
factors that are rarely found present in investigators of abstract
subjects ; they are temperament and geniality. He never
talks as if in a monologue or as if addressing empty space.
He always speaks Uke one who is weaving threads of some
idea, and these become spun out in a fascinating way that
robs the audience of the sense of time. We all know that no
iron curtain marks the close of Einstein's lecture ; anyone
who is tormented by some difficulty or doubt, or who desires
illumination on some point, or has missed some part of the
argument, is at Uberty to question him. Moreover, Einstein
stands firm through the storm of all questions. On the very
day on which the above conversation took place he had come
straight from a lecture on four-dimensional space, at the con-
clusion of which a tempest of questions had raged about him.
He spoke of it not as of an ordeal that he had survived, but
as of a refreshing shower. And such dehghts abound in his
teaching career.

It was the last lecture before his departure for Leyden
(in May 1920), where the famous faculty of science, under the
auspices of the great physicist Lorentz, had invited him to
accept an honorary professorship. This was not the first

EDUCATION 73

invitation of this kind, and will not be the last, for distinctions
are being showered on him from all parts of the world. It
is true that the universities who confer a degree on him
honoris causa are conferring a distinction on themselves, but
Einstein frankly acknowledges the value of these honours,
which he regards as referring only to the question in hand,
and not the person. It gives him pleasure on account of the
principle involved being recognized, and he regards himself
essentially only as one whom fate has ordained as the personal
exponent of these principles.

What this life of hustle and bustle about a scientist signifies
is perhaps more apparent to me, who have a modest share
in these conversations, than to Einstein himself, for I am an
old man who — unfortunately — have to think back a long way
to my student days, and can set up comparisons which are
out of reach of Einstein. Formerly, many years ago, but in
my own time, there was an auditorium maximum which only
one man could manage to fill with an audience, namely, Eugen
Diihring, the noted scholar, who was doomed to remain a
lecturer inasmuch as he went under in his quarrels with
confreres of a higher rank. But before he made his onslaught
against Helmholtz, he was regarded as a man of unrivalled
magnetic power, for his philosophical and economical lectures
gathered together over three hundred hearers, a record
number in those times. Nowadays, in the case of Einstein,
four times this number has been surpassed, a fact which has
brought into circulation the playful saying : One can never
miss his auditorium ; whither all are hastening, that is the
goal ! To make just comparisons, we must take account of
the faithfulness of the assembled crowd, as well as its number.
Many an eminent scholar has in earlier times had reason to
declare, like Faust : "I had the power to attract you, yet had
no power to hold you." Helmholtz began regularly every
term with a crowded lecture-hall, but in a short time he found
himself deserted, and he himself ^;wasjj^ well aware that no
magnetic teaching influence emanated from him. There is
yet another case in university history of a brilliant personality
who, from similar flights of ecstasy, was doomed to disappoint-
ment. I must mention his name, which, in this connexion,
will probably cause great surprise, namely, Schiller ! He had

74 EINSTEIN THE SEARCHER

fixed his first lecture in history at Jena, to which he was
appointed, and had prepared for an audience of about a
hundred students. But crowd upon crowd hustled along, and
Schiller, who saw the oncoming stream from his window, was
overcome with the impression that there was no end to it.
The whole street took alarm, for at first it was imagined that
a fire had broken out, and at the palace the watch was called
out — yet, a Httle later in the course, there was a depressing
ebb of the tide, after the first curiosity had been appeased ;
the audience gradually vanished into thin air, a proof of the
fact that the nimbus of a name does not sufiice to maintain
the interest between the lecturer's desk and the audience.

I mentioned this example at the time when Einstein's gift
for teaching had gradually increased the number of his hearers
to the record figure of 1200, yet I did not on this occasion
detect any inordinate joy in him about his success. I gained
the impression that he had strained his voice in the vast hall.
His mood betrayed in consequence a shght undercurrent of
irritation. In an access of scepticism he murmured the words,
"A mere matter of fashion." I cannot imagine that he was
entirely in earnest. It goes without saying that I protested
against the expression. But, even if there were a particle of
truth in it, we might well be pleased to find such a fashion
in intellectual matters, one that persists so long and promises
to last. The world would recover its normal healthy state
if fashions of this kind were to come into full swing. It is,
of course, easy to understand on psychological grounds that
Einstein himself takes up a sort of defensive position against
his own renown, and that he occasionally tries to attack it
by means of sarcasm, seeing that he cannot find serious argu-
ments to oppose it.

Whether Einstein's ideas and proposals concerning educa-
tional reform will be capable of reahzation throughout is a
question that time alone can answer. We must make it clear
to ourselves that, if carried out along free-thinking lines, they
will demand certain sacrifices, and it depends on the apportion-
ment of these sacrifices as to what the next, or the following,
generation will have to exhibit in the way of mental training.

An appreciable restriction will have to be imposed on the

EDUCATION 75

time given to languages. It is a matter of deciding how far
this will affect the foundations that, under the collective term
humaniora, have supported the whole system of classical schools
for centuries. The fundamental ideas of reform, which, owing
to the redivision of school-hours and the economy of work, no
longer claim precedence for languages, indicate that not much
will be left of the original Latin and Greek basis.

We have noticed above that Einstein, although he does not,
in principle, oppose the old classicism, no longer expects much
good of it. But nowadays the state of affairs is such that it is
hardly a question of supporting or opposing its retention in
fragmentary form. Whoever does not support it with all his
power strengthens indirectly the mighty chorus of those who
are radically antagonistic to it. And it is a remarkable fact
that this chorus includes many would-be authorities on
languages who have influence among us because they are
champions of the cause of retaining languages.

They do not wish to rescue languages as such, but only the
German tongue ; they point to the humaniora of classical
schools, or to Humanisterei, as they call it, as the enemy and
corrupter of their language. In what sense they mean this is
obvious from their articles of faith, of which I should like to
cite a few in the original words of one of their party-leaders :

" Up to the time of the hazardous enterprise of Thomasius
(who first announced lectures in the German language in 1687)
German scholars as a body were the worst enemies of their
own tongue. — Luther did not take his models for writing
German from the humanistic mimics who aped the old Latins.
In the case of many, including Lessing and Goethe, we observe
them making a definite attempt to shake themselves free from
the chaos of humanistic influences in Germany. — The inherit-
ance of pseudo-learned concoctions of words stretches back
to pretentious humanism as do most of essential vices of learned
styles. — The far-reaching and lasting corruption of the German
language by this poisonous Latin has its beginnings in the
humanism of the sixteenth century."

And, quite logically, these heralds extend their attacks
along the whole academic front. For, according to their point
of view, the whole army of professors is deeply immersed in
the language slime of the traditional humanism of the Greeks

76 EINSTEIN THE SEARCHER

and Latins. " The whole language evil of our times," so these
leaders say, " is at bottom due to scientists, who, in the opinion-
ated guise of a language caste, and without enriching our
conceptions in the sHghtest, seek by tinkling empty words to
give us the illusion of a new and particularly mysterious occult
science, an impression which is unfortunately often produced
on ignorant minds. . . . However many muddy outlets
official institutions and language associations may purge and
block up, ditch-water from ever new quagmires and drains
pours unceasingly into the stately stream of our language."

Thus the attack on the Latin and Greek language founda-
tion in schools identifies itself with the struggle against the
academic world as a whole, and a scholar who does defend
the classical system of education with all his might finds himself
unconsciously drifting into the ranks of the brotherhood which
in the last instance is seeking his own extermination.

This danger must not be under-estimated. It is just this
peril, so threatening to our civilization, that moves me to show
my colours frankly here. I am not a supporter of bookworm
drudgery in schools, but I feel myself impelled to use every
effort in speech and writing to combat the anti-humanists
whose password, " For our language," at root signifies
" Enemies of Science ! "

We must put no weapons into their hands, and the only
means to avoid this is, in my opinion, to state our creed
emphatically and openly after the manner of almost all our
classical writers.

This creed, both as regards language and substance, is to
be understood as being based on the efficacy of the old classical
languages. It is the luminous centre of the Hfe and work of
the men who caused Bulwer to proclaim our country the country
of poets and thinkers. The superabundance of these is so
excessive that it is scarcely fair to mention only a few names
such as Goethe, Lessing, Schiller, Wieland, Kant, and Schopen-
hauer. Our Uterature would be of a provincial standard and
not a world possession if this creed had not asserted its
sway at all times.

If the question is raised as to where our youth is to find
time for learning ancient languages under the present condi-
tions of crowded subjects, the answer is to be furnished by

EDUCATION 77

improved methods of instruction. My personal point of view
is that even the older methods were not so bad. Goethe found
himself in no wise embarrassed through lack of time in acquiring
all sorts of knowledge and mental equipment, although even as
a boy of eight years he could write in Latin in a way which,
compared with the bunghng efforts of the modern sixth-form
boy, seems Ciceronian. Montaigne could express himself
earher in Latin than in French, and if he had not had this
" Latin poison " injected into his blood he would never have
become Montaigne.

It seems to me by no means impossible that the cultured
world will one day in the distant future return to the once
self-evident view of classical languages, and indeed just for
reasons of economy of time, unless the universal language so
ardently desired by Hebbel — not to be confused with the
artificial patchwork called Esperanto — should become a reality.
But even this language, at present Utopian, but one which will
help to link together the nations, will disclose the model of the
ancient languages in its structure. Scientific language of the
present day shows where the route lies ; and this route will be
made passable in spite of all the efforts of Teutonic language
saints and assassins of humanism to block it.

The working out of ideas by research scientists leads to
enrichment of language. And since, as is quite natural, they
draw copiously on antique forms of expression, they are really
the trustees of an instruction that makes these expressions
intelHgible not merely as components of an artificial language
like Volapiik but as organic growths. That is how they pro-
ceed when they carry on their research, or describe it and
lecture on their own subject. But if they are to decide how
the school is to map out its course in actual practice, the prob-
lem of time again becomes their chief consideration — that is,
they feel in duty bound to give preference to what is most
important. Hence there results the wish to reduce the hours
apportioned to the language subjects as much as possible.

On this matter we have a detailed essay by the distinguished
Ernst Mach mentioned earlier, who exposes the actual dilemma
with the greatest clearness. He treats this exceedingly im-
portant question in all its phases, and arrives at almost the
same conclusion as Einstein. At the outset he certainly chants

78 EINSTEIN THE SEARCHER

a Latin psalm almost in the manner of Schopenhauer. Its
lower tones represent an elegy lamenting that Latin is no
longer the universal language among educated people, as it
was from the fifteenth to the eighteenth century. Its fitness
for this purpose is quite indisputable, for it can be adapted to
express every conception however modern or subtle it may be.

What a profusion of new conceptions was introduced into
science by Sir Isaac Newton, to all of which he succeeded in
giving correct and precise Latin names ! The natural inference
suggests itself to us that young people should learn the ancient
classical tongues — and yet a diferent result is coming about ;
the modern child is to be content with understanding words
with a world-wide currency, without knowing their philological
origin.

It is not necessary to be a schoolmaster to feel the in-
adequacy of this proceeding. It is true that without knowing
Arabic we can grasp the sense and meaning of the word
*' Algebra," and in the same way we can extract the essence of
a number of Greek and Latin expressions without digging at
their etymological roots. But these expressions are to be
counted in hundreds and thousands, and are increasing daily,
so that we are put before the question whether, merely from
the point of view of time, it is practicable to learn them as
individual foreign terms or as natural products of a root
language with which we have once and for all become familiar.

It is scarcely necessary for me to point out that Einstein
himself is not sparing in the use of these technical expressions,
even when he is using popular language. He assumes or
introduces terms of which the following are a few examples :
continuum, co-ordinate system, dimensional, electrodynamics,
kinetic theory, transformation, covariant, heuristic, parabola,
translation, principle of equivalence, and he is quite justified
in assuming that every one is fully acquainted with such
generally accepted expressions as : gravitation, spectral
analysis, ballistic, phoronomy, infinitesimal, diagonal, com-
ponent, periphery, hydrostatics, centrifugal, and numberless
others which are diffused through educated popular language
in all directions. Taken all together these represent a foreign
realm in which the entrant can always succeed in orientating
himself when he receives explanations, examples, or transla-

EDUCATION 79

tions, whereas with a little preliminary knowledge of the
ancient languages he immediately feels himself at home with
them ; in this we have not even taken into consideration the
general cultural value of this training in view of the access it
gives to the old Uterature and to Hellenic culture.

Perhaps I am going too far in adopting the attitude of
a laudator temporis acti towards Einstein's very advanced
opinion. We are here deaUng with a question in which nothing
can be proved, and in which everything depends on disposition
and personal experiences. In my own case this experience
includes the fact that at a very early age, in spite of the very
discouraging school methods, I enjoyed the study of Latin and
Greek, and that I learned Horatian odes by heart, not because
I had to, but because they appealed to me, and finally that
Homer opened up a new world to me. When Einstein ex-
presses his abhorrence of drill, I agree with him ; but these
languages need not be taught as if we are on parade. We see
thus that it is a question of method and not of the subject
involved. Einstein gives the subject its due by recommend-
ing a double series of classes. He allows the paths to diverge,
giving his special blessing to the group along the one without
setting up obstacles to prevent the other pilgrims from attain-
ing happiness in their own way.

We spoke of higher education for women, and Einstein
expressed his views which, as was to be expected, were tolerant,
and yet did not suggest those of a champion of the cause. It
was impossible to overlook the fact that in spite of his approval
he had certain reservations of a theoretical nature.

" As in all other directions," he said, " so in that of science
the way should be made easy for women. Yet it must not be
taken amiss if I regard the possible results with a certain
amount of scepticism. I am referring to certain obstacles in
woman's organization which we must regard as given by
Nature, and which forbid us from applying the same
standard of expectation to women as to men."

** You beUeve, then. Professor, that high achievements
cannot be accomplished by women ? To keep our attention
on science, can one not quote Madame Curie as a proof to the
contrary.? "

80 EINSTEIN THE SEARCHER

" Surely only as one proof of brilliant exceptions, more
of which may occur without refuting the statute of sexual
organization."

" Perhaps this will be possible after all if a sufficient time
for development be allowed. There may be much fewer
geniuses among the other sex, but there has certainly been a
concentration of talent. Or, in other words, totally ignorant
women have become much rarer. You, Professor, are for-
tunate in not being in a position to compare young women
of to-day with those of forty or more years ago. This I can
do, and just as once I found it natural that there should be
swarms of little geese and peacocks, I never recover from my
astonishment nowadays at the amount of knowledge acquired
by young womanhood. It requires a considerable effort on
my part very often to avoid being completely overshadowed
by a partner at dinner. The more this stratum of talent
increases, the more we have reason to expect a greater number
of geniuses from them in the future."

" You are given to prognostication," said Einstein, " and
calculate with probabilities which sometimes are lacking in
foundation. Increased education and even an increase of
talents are quantitative assumptions that make an inference
regarding higher quaUty reaching to genius appear very bold."
— A passing look of ominous portent flashed over his face, and
I noticed that he was preparing to launch a sarcastic aphorism.
So it was, for the next words were : " It is conceivable that
Nature may have created a sex without brains ! "

I grasped the sense of this grotesque remark, which was in
no way to be taken literally. It was intended as an amusing
exaggeration of what he had earher called the reason for his
faihng expectation : the organic difference which, being
rooted in the physical constitution, had somewhere to express
itself on the mental plane, too. The soul of woman strong in
impulse shows a refinement of feeling of which we men are
not susceptible, whereas the greatest achievements of reason
probably depend on a preponderance of brain substance. It is
this plus beyond the normal amount that gives promise of
great discoveries, inventions, and creations. We can just
as Httle imagine a female GaHlei, Kepler, and Descartes, as a
female Michelangelo or Sebastian Bach. But when we think

EDUCATION 81

of these extreme cases, let us also recall the balance on the
other side : although a woman could not create the differential
calculus, it was she that created Leibniz ; similarly she pro-
duced Kant if not the Critique of Pure Reason. Woman, as
the author of all great minds, has at least a right of access to
all means of education and to all advancement that is proffered
by universities. And in this connexion Einstein expressed his
wish clearly enough.

One of the most discussed themes in matters touching
school education is at the present time : ' * the selection of
gifted pupils." It has developed into a principle that is
generally recognized by the great majority, the only point
of disagreement being in respect to the number that is to be
selected.

The idea running through it is that derived from Darwin's
theory of selection : man completes the method of selection
practised by Nature. He sifts and chooses, and allows those
that are more talented to come to the fore more rapidly and
more decidedly ; he favours their advancement and makes easy
their ascent.

This principle has really always been in existence. It
started with the distribution of prizes in ancient Olympia and
reaches to the present-day examinations that are clearly in-
tended as a means of selecting talents. A greater discrimina-
tion based on a systematic search for talents was reserved for'
our own day.

It was scarcely a matter of doubt to me what attitude
Einstein would take up towards this matter. I had already
heard him say hard words about the system of examinations,
and knew his leaning towards allowing each mind to develop
its power freely and naturally.

In effect, Einstein declared to me that he would hear
nothing of a breeding of talents in a sort of sporting way.
The dangers of the methods of sport would creep in and lead to
results that had only the appearance of truth. From the
results so far obtained it was impossible to come to a final
decision about it. Yet it was conceivable that a selective
process conducted along reasonable lines would in general
prove of advantage in education, particularly in the respect
6

82 EINSTEIN THE SEARCHER

that many a talent that would ordinarily become stunted
owing to its being kept in darkness would now have an oppor-
tunity of coming to light.

This resolved itself into a talk bearing on many questions,
and of which I should like to state the main issue here. It
was specially intended to make clear the gambling method
that Einsccin repudiates, and the danger of which seems still
more threatening to me than to him.

If certain pedagogues, whose creed is force, were to have
their way, the " most gifted " pupils would be able, or would
be compelled, to rush through school at hurricane speed, and,
at an age at which their fellows were still spending weary
hours at their desks, they would have to clamber to the top-
most branches of the academic tree. All things are possible,
and history even furnishes cases of such forced marches.
Luther's friend Melanchthon quahfied at the age of thirteen
to enter the University of Heidelberg, and at the age of seven-
teen he became a professor at Tiibingen, where he gave lectures
on the most difficult problems of philosophy, as well on the
Roman and Greek writers of classical antiquity. This single
instance need only be generahzed, and we have the new ideal
rising up before our astonished gaze : a race of professorial
striplings whose upper Hps are scarcely darkened with the
down of youth ! It is a mere matter of making an early
discovery of the most gifted, and then raising the scaffolding
up which the precocious know-alls can climb as easily as
possible.

[Interposed query : Where are these discoverers of talent,
and how do they prove their own talent ? There was a good
opportunity for them in a case which I must here mention.
Einstein told me in another connexion that, as early as 1907,
that is, when he was still very young in years, he had not
only succeeded in successfully representing the Principle of
Equivalence, one of the main supports of the General Principle
of Relativity, but had even pubhshed it ; yet it made not the
sHghtest impression on the learned world. No one suspected
the far-reaching consequences, and no one pointed out this
flaming up of a new talent of the highest order. And just as
this was able to remain concealed from the learned Areopagus
of the world at that time, so a similar lack of understanding

EDUCATION 83

may easily be possible on a smaller scale at school. We know
actually that among the recognized great men of science,
there were many who did only moderately well at school ;
as, for example, Humphry Davy, Robert Mayer, Justus
Liebig, and many others. Wilhelm Ostwald goes so far as to
affirm : " Boys ordained to be discoverers later in life have,
almost without exception, been bad at school ! It is just the
most gifted young people who have resisted most strongly
the form of intellectual development prescribed by the school !
Schools never cease to show themselves to be the bitter,
unrelenting enemies of genius ! " — ^in spite of all efforts at
selection which have always been in vogue in the guise of
advancement into higher forms.]

But the new mode of selection is intended to prevent
mistakes and oversights. Is this possible ? Do not the traces
of previous attempts inspire distrust ? There was once a
very ideal selection that had to stand the test of one of the
most eminent bodies in existence, the French Academy. Its
duty was to discover geniuses on an incomparably higher
plane. It, however, repudiated or overlooked : Moliere,
Descartes, Pascal, Diderot, the two Rousseaus, Beaumarchais,
Balzac, Beranger, the Goncourts, Daudet, Emile Zola, and
many other extremely gifted people, whom it should really
have been able to find.

The only true, and at the same time necessary as well as
sufficient, breeding is carried out by Nature herself in con-
junction with social conventions, which promise the more
success the less they assume the character of incubators
and breeding establishments. If you wish to apply tests to
discover pupils of genius in any class, examine as much as
you like, excite interest and ambition, distribute prizes even,
but not for the purpose of separating at short intervals the
shrewd and needle-witted heads from the rest ; and do not
lose sight of the fact that among those who appear as the
sheep as a result of these systematized tests to discover in-
genuity there are many who, ten or twenty years later, will
take up their positions as men of eminent talent.

There is no essential difference between the forced promo-
tion of such pupils and the breeding of super-men according
to Nietzsche's recipe as exemplified by his Zarathustra.

84 EINSTEIN THE SEARCHER

Assuming that super-men are justified in existing at all,
they will come about of themselves, but cannot simply be
manufactured. Workmen, taken as a class, represent super-
men more definitely than an individual such as Napoleon
or Caesar Borgia. So the " super-scholar " exists perhaps
already to-day, not as an individual phenomenon, but as a
whole, representing his class. Whoever has had experience
in these things will know that nowadays there are difficult
subjects in which it is possible to apply to pupils of fifteen
years of age tests that are far above the plane of comprehen-
sion of pupils of the same age in former times, provided that
the average is considered, that no accidental or artificial
separation has occurred, that no pretentiously witty questions
have had to be answered, and that there has been no systematic
and inquisitive search for talent.

Let us rest satisfied if we find that the sum-total of talent
is continually on the increase. On the other hand, it is by
no means proved that we are doing civilization a service by
persisting in the impossible project of abolishing from the
world the struggle for existence prescribed by Nature. It is
an elementary fact, and one that is easy to understand, that
many talents perish unnoticed. On the other hand, observe
the long fist of eminent men who fought their way upwards
out of the lowest stages of existence only to recognize that the
difficulties that have been overcome are mostly necessary
accompaniments of talent, that is, that Nature's way of
selection is* to oppose obstacles and raise difficulties in order
to test their powers. In the case of the poor lens-grinder
Spinoza and many others ranging to Beranger, who was a
waiter, what a chain of desperate experiences, yet what
triumphs ! Herschel, the astronomer, was too poor to buy
a refracting telescope, and it was just this dispensation of
poverty that made him succeed in constructing a reflecting
type composed of a mirror. Faraday, the son of a blacksmith
without means, made his way for years as a bookbinder's
apprentice. Joule, one of the founders of the mechanical
theory of heat, started as a beer-brewer. Kepler, the dis-
coverer of the planetary laws, was descended from a poverty-
stricken innkeeper. Of the members in Goethe's circle,
Jung-Stilling, of whom Nietzsche was so fond, was a tailor's

EDUCATION 85

apprentice ; Eckermann, Goethe's intimate associate, was a
swine-herd, and Zelter was a mason. We could add many
recent names to this Hst, and very many more if we continue
the Hne backwards to Euripides, whose father was a pubHcan
and whose mother was a vendor of vegetables. This might
serve as a basis for many reflections about the *' upward course
of the talented,*' and about its less favourable reverse side.
For one might put the apparer^tly paradoxical question whether
a soaring career for many or all talents is a necessity for our
civilization, or whether it would not be better to have a sub-
stratum interspersed with talent, to cultivate a mossy under-
growth which is to serve as nourishment for the blooming
plants of the upper layer.

Maximum is not equivalent to optimum, and we learned
elsewhere that Einstein is far removed from identifying them.
In the previous case it was a question of the problem of popu-
lation ; and in the course of the discussion he mentioned that
we are subject to an old error of calculation when we regard
it as a desirable aim to have a maximum number of human
beings on the earth. It seems, indeed, that this false con-
clusion is already in process of being corrected. A beginning
is being made with new and very active organizations and
unions whose programme is to reduce the number so that an
optimum may be attainable by those left.

If we extend this Hne of reasoning still further, we arrive
at the depressing question whether too much might not be
done for talent, not only as regards breeding it, but also in
favouring the greatest number. It is quite possible that in
doing so, we might overlook, or take insufficient account of
the harm that might be done to the lower stratum, in that
we should be depriving it of forces which, according to the
economy of Nature, should remain and act in concealment.

This fear, as here expressed, is not shared by Einstein.
However brusquely he repudiates breeding, he speaks in
favour of smoothing the way for talent. " I believe," he said,
" that a sensible fostering of gifts is of advantage to humanity
generally and prevents injustice being done to the individual.
In great cities which give such lavish opportunities of educa-
tion, this injustice manifests itself less often ; but it occurs
so much the more in rural districts, where there are certainly

86 EINSTEIN THE SEARCHER

many cases of gifted youths who, if recognized as such at the
right age, would attain to an important position, but who,
together with their gifts, become stunted, nay, go to ruin, if
the principle of selection does not penetrate to their circle."

This brings us to the most difficult and most dangerous
point. The spectre of responsibiUty is rapping at the portals
of society, and is reminding us insistently that it is our duty
to see that no injustice be done to any talent that may be among
us. And this duty is but little removed from the demand that
it should be disburdened of the worries of daily life, for, so
the moral argument runs, talent will ripen the more surely the
less it has to combat these ceaseless disturbances of ordinary
Hfe.

But this thesis, so evident on moral grounds, will never be
proved empirically. On the contrary, we have good reason to
suppose that necessity, the mother of invention on the broader
scale, will often in the case of the individual talent prove to be
the mother of its best results. Goethe required for his develop-
ment an unchallenged life of ease, whereas Schiller, who never
emerged from his hfe of misery, and who, up to the time when
he wrote Don Carlos, had not been able to earn sufficient with
his pen to buy a writing-desk, required distress to make his
genius burst into flower. Jean Paul recognized this blessing
of gloomy circumstances when he glorified poverty in his
novels. Hebbel followed him along this path by saying that it
is more fruitful to refuse the most talented person the necessities
of hfe than to grant them to the least gifted. For among
a hundred who have been chosen by the method of sifting,
there will be only one on the average who will receive the
certificate of excellence in the test of future generations, for
the latter use entirely different methods of sifting from that
practised by a committee of examiners who expect ready
answers to prepared questions.

This projects us on to the horns of a severe dilemma that
scarcely allows of escape. The consciousness of duty towards
the optimum expresses itself only in a maximum of assistance,
and overhears the whispered objection of reason that Nature
has also coarser means at her disposal to attain her ends;
in her own cruelty of selection she often enough proves
the truth of Menander's saying, which, freely translated,

EDUCATION 87

says : to be tormented is also part of man's education.
The fact that Einstein — with certain reservations — favours
the giving of help to the selected few, it is for me a proof,
among many others, of his love towards his fellow-men, which
fills his heart absolutely, all questions of relativity notwith-
standing.

CHAPTER V
THE DISCOVERER

Relation of Discovery and Philosophy in History. — The Absolute and the
Relative. — ^The Creative Act. — Value of Intuition. — Constructive Activity. —
Invention. — The Artist as Discoverer. — Theory and Proof. — Classical Ex-
periments.— Physics in Primitive Ages. — Experimentum Crucis. — Spectral
Analysis and Periodic System. — The Role of Chance. — Disappointed Expecta-
tions.— ^The Michelson-Morley Experiment and the New Conception of Time.

NEXT time — so one of our talks ended — next time, as
you insist on it, we shall talk of discovery in general.
This was a promise of special import for me, for it
meant that I was to draw near to a fountain-head of instruction,
and to have an opportunity of hearing the pronouncements
of one whose authority could scarcely be transcended.

We are precluded from questioning Galilei personally about
the foundations of Mechanics, or Columbus about the inner
feelings of a navigator who discovers new lands, or Sebastian
Bach about the merits of Counterpoint, but a great discoverer
lives among our contemporaries who is to give us a clue to the
nature of discovery. Was it not natural that I should feel the
importance of his acceptance of my proposal ?

Before meeting him again I was overwhelmed with ideas
that arose in me at the shghtest echo of the word " discovery "
in my mind. Nothing, it seemed to me, could be higher :
man's position in the sphere of creation and the sum of his
knowledge can be deduced from the sum of his discoveries
which find their cUmax in the conceptions civihzation and
philosophy, just as they are partly conditioned by the
philosophy of the time. We might be tempted to ask :
which of these two precedes, and which follows? And
perhaps the ambiguous nature of this question would furnish
us with the key to the answer. For, ultimately, these two
elements cannot at all be resolved into the relationship of
cause and effect, antecedent and consequent.

THE DISCOVERER 89

Neither is primary, and neither secondary : they are in-
timately interwoven with one another, and are only different
aspects of one and the same process. At the root of this process
is our axiomatic belief that the world can be comprehended,
and the indomitable will of all thinking men, acting as an
elementary instinct, to bring the perceptual events in the
universe into harmony with the inner processes of thought.
This impulse is eternal ; it is only the form of these attempts
to make the world fully intelligible that alters and is subject
to the change of time. This form finds expression in the
current philosophy which brings each discovery to fruition,
just as philosophy bears in itself constituents of the ripe
discovery.

It seemed to me that even at this stage of my reflections I
was somewhere near interpreting Einstein's intellectual achieve-
ment. For his principle of relativity is tantamount to a regu-
lative world-principle that has left a mighty mark in the thought
of our times. We have Hved to see the death of absolutism ;
the relativity of the constituents of poHtical power, and their
mutabiHty according to view-point and current tendencies,
become manifest to us with a clearness unapproached by any
experience of earUer historical epochs. The world was far
enough advanced in its views for a final achievement of thought
which would demohsh the absolute also from the mathematico-
physical aspect. This is how Einstein's discovery appeared
as inevitable.

Yet a shadow of doubt crossed my mind. Einstein's
discoveries came to light in the year 1905 — that is, at a time
when hardly a cloud was visible to forewarn us of the storms
which were to uproot absolutism in the world. But what if a
different kind of necessity had imposed itself on world-history,
and hence on the world-view ? Nowadays we know from
authentic accounts, which no one doubts, that all that we have
experienced during the war and the revolution has hung upon
the activities of one frail human being of quite insignificant
exterior, a bureaucrat of the Wilhelm-Strasse, a choleric eccen-
tric who succeeded in frustrating the Anglo-German alliance
which was unceasingly being pressed upon us for six long
years after the beginning of the century.

Amid the noisy progress of universal evolution the secret

90 EINSTEIN THE SEARCHER

and insignificant nibbling of a mole cannot be regarded as of
momentous importance for history, and yet if we eliminate it
from the complete picture of events we find as a result that all
our experiences have been inverted. Absolutism would not
have been thrown overboard, but would probably have kept
the helm with greater mastery than ever as the exponent of an
Anglo-German hegemony of the world, and a political outlook
fundamentc^lly different in tendency would now have been
prevailing on the earth.

But Einstein's Theory of Relativity would not have taken
the slightest heed of this. It would have arisen independently
of the current forms of political conceptions, simply because
we had reached that point in our intellectual development and
because Einstein was Uving and spinning his webs of thought.
And the question whether his theory will also have crushed
absolutism for the non-physicist cannot be answered.

It may indeed be doubted whether its time had already
come. In the case of many important events in the history of
thought their moment of birth can be fixed to within about
ten years, as for example the Theory of Evolution, which had
been conceived in several minds at the same time and had of
necessity to come to life in one of them, even if it had failed in
the case of the others. I venture to say that without Einstein,
the Theory of Relativity in its widest sense, that is, including
the new doctrine of gravitation, would perhaps have had to
wait another two hundred years before being born.

This contradiction is cleared up if we use sufficiently great
time intervals. History does not adapt itself to the time
measures of politics and of journalism, and philosophies are
not to be calculated in terms of days. The philosophy of
Aristotle held sway right through the Middle Ages, and that
of Epicurus will gain its full force only in the coming genera-
tion. But if we make our unit a hundred years the connexion
between philosophies and great discoveries remains true.

Whoever undertakes to explore the necessity of this con-
nexion cannot evade the fact that the lines of the result had
been marked out in the region of pure thought, as can be proved,
before even the great discovery or invention was able to present
it in a fuUy intelligible form. Even the achievement of Coper-
nicus would follow this general rule of development : it was

THE DISCOVERER 91

the last consequence of the belief in the Sun Myth which had
never been forsaken by man in spite of the violent efforts of
the Church and of man himself to force the geocentric view.
Copernicus concentrated what had survived of the wisdom of
the earliest priests — which includes also the germ of our modern
ideas of energy and electricity — of the teachings of Anaxagoras
and the Eleatics which had remained latent in our conscious-
ness : his discovery was the transformation of a myth into
science. Mankind, whose wandering fancy first feels pre-
sentiments, then thinks and wishes to know, is a large edition
of the individual thinker. The latter sees further only because
he, so to speak, stands on the shoulders of a sum-total of beings
with a world-view.

Let us turn our attention to an example from the most
recent history of philosophy and discovery. The absolute
continuity of events was one of the generally accepted canons
of thought, and is even nowadays taught by serious philo-
sophers as an incontrovertible element in our knowledge. The
old quotation Natura non facit saltus, popularized by Linn^,
is one of the formulae of this apparently invincible truth. But
deep down in the consciousness of man there has always been
an opposition to it, and when the French philosopher Henri
Bergson set out to break up this Une of continuity by meta-
physical means in ascribing to human knowledge an inter-
mittent, cinematographic character, he was proclaiming in an
audible and eloquent form only what had lain latent in a new
but as yet incomplete philosophy. Bergson made no new
" discovery," he felt his way intuitively into a new field of
knowledge and recognized that the time was ripe for the real
discovery. This was actually presented to us in our day by
the eminent physicist Max Planck, the winner of the Nobel
Prize for Physics in 1919, in the form of his " Quantum Theory."
This is not to be taken as meaning that a revolutionary philo-
sophy and a triumph of scientific research now become co-
incident, but only that a discontinuous, intermittent sequence,
an atomistic structure, was proved by means of the weapons
of exact science, to be true of energies which, according to
current behef, were expected to be radiated regularly and
connectedly. This was probably not a case of the accidental
coincidence of a new philosophical view with the results of

92 EINSTEIN THE SEARCHER

reasoning from physical grounds, but a demand of time, exact-
ing that the claims of a new principle of thought be recognized.

As above suggested, it is more difficult to i&nd a link between
Einstein's discoveries and antecedent presentiments of rela-
tivity. For a mere reference to the downfall of absolutism
in the world of human events will not suffice. In the case of
Einstein, we see such a tremendous rush of thought in one
being that we almost feel compelled to recognize an^ analogy
with the Quantum Theory and believe in a discontinuity in the
course of intellectual history. Yet there are certainly threads
that connect Einstein's achievement with a prophetic insight.
In this case, however, we must spread out over centuries what
in the case of other discoveries extends, in comparison, only
over decades. That doubt of Faust, which troubles the spirit
of every thinker : ** whether in yonder spheres there is also an
Above and a Below,'* and which goes back as far as Pyrrhon
and Protagoras, is itself relativistic ; it expresses doubt whether
the co-ordinate system passing through our own lives as centres
is vahd. It is ultimately a matter of point of view, and the
mathematico-physical consequences of the endless series of
questions, and the relation, which arises from the couple,
Above-Below, probably leads to a new mode of comprehending
the constitution of the world, for which Einstein's creative
work found the adequate expression in abstract terms. And
from this point onwards, in accordance with the principle of
reciprocal action, a new stream of knowledge will pour itself
into the hazy stretches of philosophy. A fundamental and
radical reform of our philosophy seems inevitable, particularly
with respect to our conceptions of Space and Time, perhaps,
too, even with respect to Infinity and CausaHty. Much dross
will have to be sifted out of our old categories of thought and
out of our world wisdom, which once served as material for fine
structures. What will the finer ones look Hke that are to take
their places in obedience to the command of physics ? Who
would care to take it upon himself to form an estimate ?

Much will be uprooted, and it is possible that even the
defiant *' ignorabimus," the antipole of the search for truth
from Pyrrhon to Dubois, will again take up the cudgel. For
in the face of despairing uncertainty there is the one certainty :
what cannot be comprehended is being encircled more and more

THE DISCOVERER 98

by the great discoverers ! And even if the absolute point of
convergence can never be reached, there is within our reach at
least another point which is a haven of rest in the passing
stream of philosophies, namely, a moral centre around which
eddies of happiness circle. At the heart of this world- view
there is the uplifting belief in an advance of knowledge in
spite of all, and a belief in the vanishing of age-long problems
and difficulties under the flood of discoveries. And even if
afterwards and concurrently ever new problems and diffi-
culties arise, these do not suppress our feeling of triumph.
Every achievement in this field gives us a sense of enfranchise-
ment from prejudices, not the least of which is narrowness of
national outlook. Not only do discoverers construct bridges
of thought that stretch to astronomical distances, but, what is
more difficult, they build bridges for our feehngs, that sur-
mount poHtical obstacles. Every thinking being who plays a
part in the making of some great discovery and who, with
deepened vision, bows before a new achievement of mind,
gradually becomes a disciple of the rehgion of universal
politics, the creed of which is faith in the brotherhood of
thought. The nucleus of a philosophy that belongs to the
future is the recognition that differing national view must be
compounded into a unity, and that every great discovery
means a step towards attaining this end.

Even if we accept Pascal's wonderful dictum that human
knowledge is represented by a sphere which is continually
growing and increasing its points of contact with the unknown,
we must not interpret it as a sign of despair. It is not the
enlargement of the unknown, but only that of knowledge that
stirs our feelings with ethical forces. The positive calls up in
us a living force by inspiring in us the feeling that the sphere
of knowledge is destined to grow, and that there can be no
higher duty for all the energies of mind than to obey the call
for combined action towards this growth which will bring the
world into harmony.

Full of such reflections I entered the home of the great
discoverer, whose activities unceasingly hovered before my
vision as ideal examples of creative effort. I discovered him,
as almost always, seated before loose sheets of paper which his
hand had covered with mathematical symbols, with hiero-

94 EINSTEIN THE SEARCHER

glyphics of that universal language in which, according to
Galilei, the great book of Nature is written.

What a very different picture many an outsider draws of
the manner in which a seeker in the heavens works ! He is
imagined hke Tycho Brahe to be surrounded by unusual
pieces of apparatus, spying through the ocular of a long range
refractor into the universe, seeking to unravel its ultimate
secrets. The true picture does not correspond to this fancy
in the sUghtest. Nothing in the make-up of the room reminds
one of super-earthly subUmity, no abundance of instruments
or books is to be seen, and one soon becomes aware that here
a thinker reigns whose only requirement for his work, which
encompasses the world, is his own mind, plus a sheet of paper
and a pencil. All that acts on the observatories outside, that
gives rise to great scientific expeditions, that, indeed, ulti-
mately regulates the relationship of mankind to the con-
stitution of the universe, the revolution in the knowledge of
things connecting heaven and earth, all this is here con-
centrated in the simple figure of a still youthful scholar, who
spins out endless threads from the fabric of his mind : the
words of a poet are recalled to our memory, which, addressed
to all of^us, have been fulfilled to the last degree by one living
among]us : —

" Whereso thou roamest in space, thy Zenith and Nadir unite thee —
This to the heavenly height, that to the pole of the world, —
Whatsoever thou do, let thy will mount up into Heaven —
But let the pole of the world still o'er thine actions preside."

(Schiller i Translation by Merivale.)

And this one helped to fulfil this aim and I must break off
his thread of thought to put the question : What is Discovery,
and what does it signify ?

It is a purely abstract question that may appear to many
to be devoid of content. Such will repeat to themselves, as
best they can, the list of discoveries and think a man makes
a discovery when he finds out something important, such as
the Laws of Falhng Bodies, the formation of Rainbows, or the
Origin of Species : a general denomination may be found for
it perhaps only by ascribing to Discovery something requiring
a powerful mind, a creative genius.

At first it staggered me to hear Einstein say : " The use of

THE DISCOVERER 95

the word * Discovery * in itself is to be deprecated. For
discovery is equivalent to becoming aware of a thing which is
already formed ; this links up with proof, which no longer
bears the character of * discovery ' but, in the last instance, of
the means that leads to discovery." He then stated at first
in blunt terms, which he afterwards elaborated by giving de-
tailed illustrations : " Discovery is really not a creative act ! "

Arguments for and against this view flashed through my
mind, and I thought involuntarily of a great master of music
who, when he was asked : " What is Genius ? " answered :
" A genius is one to whom ideas occur." This parallel might
be carried still further, for I have repeatedly heard Einstein
call " ideas " what we would regard as wonderful thoughts.
Does not the philosopher Fritz Mauthner speak of the discovery
of gravitation as being an ** aper9u " of Newton ; yes, in the
sense of aperfus as appHed in ancient Greek philosophy, and
which included almost everything that was left by Pythagoras,
Herachtus, etc., as a token of their genius. On the other hand,
we are all possessed of the desire to differentiate clearly
between an idea and a creative act of thought, as occurs in
Grillparzer's aphorism : "An idea is not a thought ; a thought
knows its bounds, whereas the idea leaps over them and
succeeds in accomplishing nothing ! "

Here, then, we must revise our view. We know, for ex-
ample, how much Einstein's " ideas," felt by him to be such
and named so accordingly, accompHshed. Let us hear how
he characterizes in a few words his own " idea " which shook
the world :

" The underlying thought of relativity," he said, in con-
nexion with this question, " is that there is physically no
unique (specially favoured) state of motion. Or, more exactly,
among all states of motion there is none that is favoured in
the sense that, in contradistinction to the others, it may be
said to be a state of rest. Rest and Motion are not only by
formal definition but also by their intrinsic physical meaning
relative conceptions."

" Well, then," I interposed, " surely this was a creative
act ! This first flashed across your mind, Professor ; it re-
presents your discovery, so that we may well let the word
retain the meaning usually associated with it I "

96 EINSTEIN THE SEARCHER

" By no means/' answered Einstein, " for it is not true
that this fundamental principle occurred to me as the primary
thought. If this had been so perhaps it would be justifiable
to call it a " discovery." But the suddenness with which
you assume it to have occurred to me must be denied. Actu-
ally, I was lead to it by steps arising from the individual laws
derived from experience."

Einstein supplemented this by emphasizing the conception
" invention," and ascribed a considerable importance to it :
" Invention occurs here as a constructive act. This does not,
therefore, constitute what is essentially original in the matter,
but the creation of a method of thought to arrive at a logically
coherent system . . . the really valuable factor is intuition \ "

I had thought, long and intently, about these theses to
discover as nearly as possible what distinguished their content
from the usual view. The fundamental differences suggest
an abundance of ideas whose importance grows in value as
we apply them to various cases as illustrations. And I feel
convinced that we shall yet have to occupy ourselves with
these words of Einstein, which present themselves as a con-
fession, as with the famous " hypotheses non fingo " that
Newton set up as the idea underlying his work.

The latter as well as the former implies something negative :
it denies something. In Einstein's words there is apparently
a repudiation of the really creative act in discovery ; he lays
stress on the gradual, methodical constructive factors, not
omitting to emphasize intuition. There is no other course
open to us but to seek indirectly a synthesis of these concep-
tions, and to eliminate what is apparently contradictory in
them.

I consider this possible if we decide to subdivide the dis-
covery into a series of individual acts in which succession
takes the place of instantaneous suddenness The creative
factor may then remain intact ; indeed, it attains a still higher
degree of importance if we imagine to ourselves that a series
of creative ideas must be linked together to make possible a
single important discovery.

The original idea never springs fully equipped and armed
like Minerva out of the head of its creator. And it is wise
to bear in mind that even Jupiter had to suffer in his head

THE DISCOVERER 97

a period of pregnancy accompanied with great pain. It is
only in the after-picture that Pallas Athene appears with the
attribute of suddenness. It is the nature of our myth-building
imagination to leap over the actual act of birth so as to give
a more brilliant form to the finished creation.

We feel great satisfaction when we learn that Gauss, the
Prince of Mathematicians, declared in one of his valuable
flashes of insight : "I have the result, only I do not yet know
how to get to it." For in this utterance we see above all
that he emphasizes a lightning-Uke intuition. He has posses-
sion of a thing, which is, however, not yet his own, and which
can only become his own when he has found the way to it.
Is this contradictory ? From the point of view of elementary
logic, certainly ; but methodologically, by no means. Here
it is a question of : Erwirh es um es zu hesitzen I This makes
necessary a series of further intuitions along the road of
invention, and of construction.

This is, then, where that phase commences, which Einstein
denotes by the word " gradual," or "by steps." The first
intuition must be present ; its presence as a rule usually
guarantees that further intuition will follow in logical sequence

This does not always happen. In passing, we discussed
several special cases from which particular inferences may
be drawn. The powerful mathematician Pierre Fermat has
presented the world with a theorem of extremely simple form
which he discovered, a proof of which is being sought even
nowadays, two and a half centuries after he stated it. In
easy language, it is this : the sum of two squares may again
be a square, for example, 52-1-122=132, since 25+144=169;
but the sum of two cubes can never be a cube, and, more
generally, as soon as the exponent, the power index n, is
greater than 2, the equation x^'+y^'^z" can never be satisfied
by whole number values for x, y, and z ; it is impossible to
find three whole numbers for x, y, and z, which, when sub-
stituted in the equation, give a correct result.

This is certainly true ; it is an intuitive discovery. But
Fermat 's assertion that he possessed a " wonderful proof,"
is for very good reasons open to contradiction. No one
doubts the absolute truth of the theorem. But the later
inspiration, the next step after the intuition, has occurred
7

98 EINSTEIN THE SEARCHER

neither to Fermat nor to anyone else. It cannot be established
whether his remark about the proof was due to a subjective
error, or was baseless. In any case it seems probable that
Fermat had arrived at the result per intuitionem without
knowing the way to it. His creative act stopped short ; it
was only a first flare of a conflagration, and did not fulfil
the condition that Einstein associates with the conception
of a logically complete method.

We may, indeed, pursue this case of Fermat still further.
He had enunciated another theorem, again per intuitionem,
namely, that it was possible to construct prime numbers of
any magnitude by a formula he gave. Euler later showed
by a definite example that the theorem was false. It was
stated in a letter to Pascal written in 1654 ^^ the words : the
result of squaring 2 continuously and then adding i must
in each case be a prime number, that is, 2.^^-\-i must always
be a prime no matter what value k may have. Fermat added :
** This is a property for the truth of which I answer." Euler
chanced to try ^=5, and found that 2^^+1 = 4,294,967,297,
which may be represented as the product of 641 and 6,700,417,
and hence is not a prime.

It is conceivable that no Euler might have Uved, and that
no one else might have discovered this contradiction. What
would then have been the position of this '* discovery " of
Fermat ?

We should certainly not have disputed its creative character,
for we should have said that it corresponds to a fact which
is fully formed, but cannot be proved. But now that we
know that the fact does not exist at all, the thing assumes a
different colour. It was not a discovery at all, but an erroneous
conjecture. But one would never be able to arrive at an
erroneous conclusion of this sort without being a mathe-
matical genius, and having the inspiration of the moment.
And from this again it follows that to make a discovery in
the full sense of the word the intuition of the moment does
not suffice, but must be supported by a series of intuitions,
and this is the condition that it become a permanent com-
ponent of universal truth.

The fact that Einstein refers to the action of " inventing "
in his explanation, gives support, it seems to me, to the view

THE DISCOVERER 99

that, strictly speaking, discovering and inventing are never
to be regarded as being separable. In discovering, what has
to be constructed persists, and in inventing, it is a question
of finding the path along which there is the promise of success,
be it by a method, a proof, or by some general work. We
spoke of works of art, and I was delighted to see that Einstein
was by no means disinclined to claim certain works of pure
thought, which are usually placed in the category of scientific
discovery, as works of art. In the latter, however, the pure
process of invention plays the prominent part, for in them
something is represented that did not exist at all before ;
this has repeatedly led to the artist's achievement being given
the higher rank, as being properly and exclusively creative.
The argument runs somewhat along these lines : the infinites-
imal calculus would certainly have been discovered even
if there had been no Newton and no Leibniz, but without
Beethoven we should never have had a C Minor Symphony,
and never in the future would it have appeared, for it was a
subjective, absolutely personal, and unique product of its
creator.

I believe this may be admitted, and that we may neverthe-
less retain the view that in the work of art, too, the act of
discovering is to be found. Let us consider for a moment the
elementary substance of the first movement of this fifth
symphony, a colossal movement of 500 bars, which expresses
itself quite definitely in four notes, of which one is repeated
three times. " Thus Destiny thunders at the gates " is
Beethoven's motto for this section ; it is expressed tonally
in a succession of notes which through all eternity existed
among the possible permutative arrangements of these sounds.

Beethoven, so it is expressed, invented it. But it is just
as correct to say — in Einstein's words — " he became aware of
what was already formed " — that is, he " discovered " the
fundamental theme, and afterwards " proved it " in terms of
musical logic unheard-of beauty in a methodical elaboration.
We may, indeed, go further still. This motif of four tones was
not only extant as an abstractum, as a possible mathematical
arrangement, but also as something natural. Czerny, a
pupil of Beethoven, to whom the master confided many a
remark about the origin of his compositions, reports that a

100 EINSTEIN THE SEARCHER

bird, the yellow-hammer, had sung this theme to Beethoven
in the woods. But neither the bird nor any other Hving
creature had invented it ; rather what could not be created,
because it had always been in existence, became objectified
in the medium of sound. Beethoven found it ; it was res
nullius when he found it and when he discovered simultaneously
with the succession of tones that they were appropriate for a
powerful nmsical representation of sombre Destiny. Every
theme, be it of Beethoven, Bach, Wagner, or anyone else, may
be represented graphically by a curve (in the case of Bach's
fugal themes this has, in fact, been done for special purposes),
and just as it is certain that every elliptic-arc existed before
all geometry, so it may be affirmed with equal certainty that
everything musical was in existence before the advent of
composition, and was merely waiting for a discoverer whom
we designate the inventor, the creative organ.

But may not some of this glory be reflected on to scientific
discovery ? When we are in an ecstasy of admiration, we
talk of a creative act as of something divine ; may we not
also grant to the scientist this tribute which, owing to a shght
confusion of conceptions, we shower on the artists ? And I
believe that Einstein's definition does not set up an insuperable
barrier in this respect to our admiration, which exerts every
effort to pass beyond, refuses to come to a standstill before
the rigid fact that the discoverer reveals only what is pre-
formed ; our emotions prove to be stronger than our minds
with their objective valuation. In the last instance, we opine,
the scientific discoverer, too, creates something new, namelj^ a
piece of knowledge that was previously not in existence. And
we obey the impulse of hero-worship, when we call a definite
first discoverer a creator.

This silences opposition certainly only for a time, without
vanquishing it. For this knowledge, too, lay ready before
the first discoverer appeared : he did not create it, but merely
drew back the veil that enveloped it. So that, ultimately,
we get back to " intuition " in its Hteral sense, a becoming
aware of things, an exact consideration of things, states, and
relationships ; and this intensive consideration, full of wonder-
ment, has always been a privilege of a very few chosen men.

It might be asked : Was there any knowledge of Pythagoras*

THE DISCOVERER 101

Theorems before Pythagoras gave us his proof ? We should
have to answer : It was in existence at least in the still dark
field of vision of Pythagoras, which became illumined one
day when he took such a view of the number-ratios 3 — 4 — 5
that an exact intuition could actually come about. It is
erroneous to assume that a creative act suddenly called up
before his soul as if by magic the figure with the three squares
drawn externally on the sides of a triangle. Rather, he " took
his stride " (as we know from Vitruvius) by considering a
triangle whose sides were of a definite length ; and the well-
known proof, which is linked indissolubly in our minds with
his work, is not his at all, but Euclid's. Yet our annals grow
musty, centuries pass by, and the credit of being the creator
rests with the man who first succeeded in getting a clear
picture of such a triangle.

It seems natural to test discoveries by experiments. The
first result of doing this is a very remarkable increase in the
rate at which the intuitive process has developed. In ancient
times, intuition, it seems, scarcely felt the need of proving
things by experiment ; all that was discovered by Archimedes
in mechanics, by the Pythagoreans in acoustics, by EucHd in
optics, may be reduced practically to the formula *' heureka,*'
and it is probably scarcely an exaggeration to say that more
and more fruitful experiments are performed in one week
nowadays than in the whole of the classical age taken together.*

* Recently certain precisians in definition have been seeking to establish
a fundamental difference between physicists of reality, experimental physicists,
and " blackboard-physicists." The last term is given jeeringly to theoretical
physicists because they, in the opinion of these critics, wish to found Nature
entirely on formulae argued out on the blackboard. The history of science
does recognize this distinction, although it is, of course, quite possible for a
physicist to arrive at important discoveries without making any experiments.

One might be more justified in asserting that the great theorist need not
necessarily be a great experimenter and vice versa. But I can quote no
example of a physicist who confined himself obstinately to blackboard dis-
cussion, and on principle disowned all experimental work.

I must add that Einstein himself is fond of experimenting, and has had
much success in experimental work. The amount of advice and encourage-
ment that he has given, and still gives, to many workers in this field is very
considerable. But he does not practise experimental work regularly, and
remarked that he is obhged to appeal to outside help for certain practical tests.
There are specific experimental geniuses, whose activity assumes the happiest
and most fruitful form when it supplements that of the theorist and fertilizes it.

102 EINSTEIN THE SEARCHER

Experiments have become, if not the sole, yet the most definite,
test of intuition. I need only recall the observations of the
solar eclipse of 1919, which were of an experimental character
inasmuch as they used apparatus to question Nature. To the
world generally, they gave the irrefutable confirmation of
Einstein's Theory of Gravitation, but not to Einstein himself,
whose intuition felt itself so certain that the confirmation was
a mere matter of course.

But this is not the average case ; in many cases the in-
tuition of the discoverer appeals to experiment as a judge of
great authority, who is to confirm, reject, or correct.

Let us take some examples of cases in which the intensity
and the value of intuition were measured by the experimental
results. Benjamin Franklin's Kite Experiment may be taken
as a classical instance. Here is a man in whose head the idea
takes root that lightning and electricity are one and the same
thing. Innumerable persons before and after his time might
have hit on the same idea, which is now the common knowledge
of children. Yet, a single man had to appear who became
aware of this pre-formed fact and who simultaneously thought
out a method of putting it to proof. In 1752 he constructed
a kite, sent it up into the clouds during a storm, and caught up
sparks on the ground by a metalHc contrivance, and, as d'Alem-
bert so aptly described it to the French Academy :

" Eripuit coelo fulmen ..."

He wrested the lightning from the heavens. Jupiter tonans
illuminated a great discovery, a mighty intuition which had
entered like a lightning stroke into the brain of a discoverer.

This case would be classical, were it not that nine-tenths of
it is based on legend. Franklin was by no means the first who
had this intuition, and his experimental test was so full of
faults that it was within an ace of faihng. Franklin used a dry
thread of hemp, which he thought to be a conductor, but
which became a conductor only after it had been made wet by
rain. Till that moment the exhibition of sparks on the ground
had been poor enough, and little was wanting for Franklin
to give up his attempt and confess that he had been inspired,
not with an intuition, but with a hallucination.

But to whom then is the glory of this discovery due ? This

THE DISCOVERER 103

is a difficult point to decide. As early as 1746, that is, six years
before Franklin's kite made its ascent in Philadelphia, Professor
Winkler of Leipzig had asserted in a dissertation that the two
phenomena were identical, and had proved this theoretically ;
and three years earher still Abbe NoUet had declared the
storm clouds to be the conductors of an electrical induction
machine. Almost simultaneously with Franklin, Dalibard,
Delor, Buffon, Le Monnier, Canton, Bevis, and Wilson made
experiments on an elaborate scale, which far exceeded that of
FrankHn in their results. To this must be added that the
experiment was conducted with evident success only in 1753,
when de Romas of Nerac in South France wove a real conductor
of thin annealed wire into the kite-string, and succeeded in
bringing down a regular thunderstorm with flashes of lightning
ten feet long, accompanied by a deafening uproar. It was only
then that the track of the inspiration was traced back through
time to the Roman Kings, Numa Pompilius and TuUus Hosti-
lius, as the first experimenters with lightning. And then the
physicist Lichtenberg sought to furnish a proof that the old
Hebrew ark of the Covenant, together with the tabernacle, were
nothing other than great pieces of electrical apparatus highly
charged with electricity derived from the air ; thus the first
intuition, and the priority of discovery, would have to be
ascribed to Moses or Aaron ! And connected with this was
the fact, supported by substantial proof, that the Temple of
Solomon was protected by lightning-conductors.

I must not omit to mention that Einstein regards this
whole chain of proofs stretching back to early times as by no
means established, although besides Lichtenberg, other im-
portant scholars, such as Bendavid in Berlin and MichaeHs in
Gottingen, have vouched for their truth. And as it is a matter
of electrical relationships, Einstein's doubts cannot be passed
over. As far as I recollect, they were not directed against
the rough facts in themselves, but against the sense that is
construed into them — that is to say, in the case of both the
ancient Roman and the Biblical data, the conception of dis-
covery must be excluded, and must be awarded rather to those
intellectual efforts which have led to the creation of a method
of thought. None the less, we may uphold our statement that
in this case, presumed to be classical, neither Franklin nor any-

104 EINSTEIN THE SEARCHER

one else is to be claimed as the discoverer or as the central
figure in a creative act.

The experimental case of spectral analysis is incomparably
simpler and less open to dispute. It is without doubt a dis-
covery of fundamental importance bearing all the character-
istics of originaHty, for no predecessors are discernible. I have
always felt a little dissatisfied with the fact that it required
two men to think it out, that a duo of minds was necessary for
one act of thought which appears quite uniform, elementary
and inseparable from the intuition of a single mind. But it
seems possible that tradition has not handed the facts down to
us faithfully, and that the two men, with a unanimity arising
from their partnership in work, combined their results, which
were not, at the beginning, of a dual character. This possibiUty
became clear to me from a remark of Einstein which made it
plain to me that the conjunction Kirchhoff and Bunsen is to
be taken as denoting Kirchhoff and then, after a pause, Bunsen
in the next breath ! But if we discard this question of unity
or duaUty, we are left with the fact that the idea of a spectral
analysis occurred to some one (as a result of preceding optical
experiments with Fraunhofer lines), and was fully confirmed
by later experiments. Only fully confirmed ? No, the classic
rank of this case manifested itself in a much more triumphant
manner, for it is impossible that the intuition of Kirchhoff
and Bunsen could have grasped the whole significance and
range of their discovery even after they had made it their
own.

Every discovery encloses a germ of hope. However great
this may have been in the case of Kirchhoff, it could not by any
stretch of imagination approach the degree of its fulfilment.
The fundamental theoretical idea that '' a vapour absorbs from
the ray-complex of white fight only those wave-lengths which
it can emit " gave rise to a process, the ingenuity, deficacy,
and certainty of which is almost inconceivable. When rays
of fight emitted by incandescent vapour were separated by a
prism, there were discovered fine coloured lines that betrayed
some unknown mystery. The spectroscopic experiments
proved, in a succession of results, that the author of the above
idea had made not only one discovery, but a whole host of them.
For example, it was observed that, in burning minute residues

THE DISCOVERER 105

obtained by evaporating certain mineral waters, a red line and
a blue line that had never been seen before appeared in the
spectrum. One knew immediately that an element, hitherto
undiscovered, was proclaiming its presence. In this way in
quick succession the element Caesium was discovered, then
Rubidium, ThaUium, Indium, Argon, HeUum, Neon, Krypton,
Xenon — certainly things that were already pre-formed in
Nature, just as the idea of a bridge from Optics to Chemistry
lay all ready in the heart of Nature ; but no blame can be
given to the astonished contemporaries who regarded this
fundamental discovery of spectroscopic analysis as a creative
achievement of the intellect.

This ray of hope gave a glimpse of the degree of accuracy
attainable. In this connexion the experiment confirmed
inj&nitely more than the boldest imagination could ever have
dreamed. A yellow line was detected in the spectrum of
sodium. And it was found experimentally that the three-
millionth part of a thousandth of a gramme of a sodium salt
is sufficient to produce this sodium line in the spectrum of a
Bunsen burner. There commenced a dizzying passage in the
Calculus of Probabilities for, since it was found that in the
sun's atmosphere hydrogen, carbon, iron, aluminium, calcium,
sodium, nickel, chromium, zinc, and copper were present, the
question arose as to how great was the possibility of an error
in this observation. Kirchhoff calculated it as a chance of a
trillion to one that these substances are actually present in
the sun !

Never before had an experiment verified to such an extreme
degree a discoverer's idea. It seems appropriate at this stage
to deal with a doctrine which seeks to shed light into the deepest
recesses of the connexion between experiment and discovery.
It teaches that an experimentum cruets, an experiment that
verifies absolutely, is impossible in physics. That is to say,
every idea of a discoverer involves a hypothesis, and, how-
ever the experiment that follows may turn out, there still
remains the possibility that this hypothesis was false, and may
later have to make way for another essentially contradictory
hypothesis which will be valid again only for a limited time.

The chief exponent of this theory is the eminent scholar,
Pierre Duhem, Membre de ITnstitut. He 'draws a parallel

106 EINSTEIN THE SEARCHER

between experiment and mathematical proof, particularly with
the indirect, apagogic form which has been so successfully
apphed in EucHdean geometry. In this method it is assumed
that a certain statement is erroneous ; it is then shown that
it leads to an obvious contradiction ; consequently the state-
ment was correct provided that a certain doubt be excluded.
Thus in the domain of mathematics we have a real experi-
mentum cruets.

In accordance with this, Duhem tests the vahdity of two
physical theories, both of which were put forward and claimed
as discoveries. Newton had discovered the nature of light to
consist in " emission " ; to him, as well as to Laplace and Biot,
light consists of projectiles that are emitted with very great
velocity. The discovery of Huyghens, supported by Young
and Fresnel, substitutes wave-motion in place of corpuscular
emission. Hence, according to Duhem, we have, or we had,
here two hypotheses which appear to be the only ones possible.
Experiment was to pronounce a judgment, and at first it
decided irrefutably in favour of the wave-theory. Therefore,
the discovery of Huyghens is alone true, and that of Newton
is shown to be an error ; there is no third outlet, and so we
have quite certainly an exferimentum crucis before us.

The term itself originates in Bacon's Novum Organum,
Contrary to Duhem's assumption, it does not refer to a signpost
at cross-roads giving various routes, nor is it connected with
croix ou pile, heads or tails. Experimentum crucis denotes
rather a divine judgment at the cross, that is a test that is
absolutely decisive and beyond further appeal. But no ! adds
Duhem, there is no room for a third judgment in the case of
two contradictory statements in geometry, but there is between
two contradictory statements in physics. And, in fact, this
third possibiUty has manifested itself in the discovery of
Maxwell, who has shown that the nature of hght is founded
on a process of periodic electromagnetic disturbances. Hence,
so concludes Duhem, experiment can never decide whether a
certain theory is alone valid. The physicist is never certain
that he has exhausted all conceivable possibilities of thought.
The truth of a physical statement, the validity of a discovery,
cannot be confirmed by any experimentum crucis.

According to this argument, therefore, it is also possible

THE DISCOVERER 107

that the scientific grounds of spectral analysis do not conform
to truth. A contradictory hypothesis may, indeed, be set
up, with the result that the same experiments that had led
Kirchhoff' s discovery from one triumph to another would have
to be interpreted in a totally different sense.

I must frankly confess that I cannot subscribe to such an
extreme eventuality, since, in my opinion, Duhem's analogy
with mathematics excludes this possibility. For if a certain
probability is expressed by a trillion to one, then I venture to
state that even in the case of mathematical truths certainty
reaches no higher degree of probability. From the history of
mathematics we know of theorems which were enunciated
and provided with complete proofs, and yet did not succeed
in establishing themselves ; hence we see that, however evident
a mathematical theorem may be, it is still only a matter of
very great probability.

If, following our usual habits of thought, we take this for
absolute certainty, then we may also consider the sum-total
of experiments in the realm of spectral analysis to be a great
experimentum crucis for the correctness of the theory itself.

Far removed from it, and yet connected with it, there is
the '* Periodic System of the Elements," the discovery of
Mendelejew and Lothar Meyer. It, too, offered prophetic
glances into the future, foretold the unknown, hinted at things
that were present only in imagination in a scheme of thought
that assigned definite places of existence to undiscovered things.
The Periodic System is represented by a table containing
vertical and horizontal rows, in the squares of which the
elements are entered according to certain rules depending on
their atomic weights. The discovery consisted theoretically
in stating that the physical and chemical properties of each
element is the arithmetic mean between the properties of its
horizontal and vertical neighbours. This gave rise to pre-
dictions concerning the unoccupied squares. These gaps,
these blank spaces in the table, seem to say prophetically :
There are elements missing here that must be discoverable.
The neighbours will betray them, and the empty space itself
shows by what means they are to be found. With the shrewd-
ness of a detective, Mendelejew was able to say : There must
be elements of the atomic weights 44, 70, and 72 ; we do not

108 EINSTEIN THE SEARCHER

know them yet, but we are in a position to determine the
properties of these foundlings of the future, and, what is more,
the properties of their compounds with other elements. Later
researches, which led to the discovery of the elements.
Scandium, Gallium, and Germanium, have actually confirmed
all these predicted properties.

The metal Gallium was discovered in 1875 by spectroscopic
means. Its properties are the mean of those of Aluminium
and Indium, and this places it in a position which had already
been assigned to it in the periodic table before its discovery ; for,
owing to a gap in the system, Mendelejew had asserted its
existence five years previously, although he then knew nothing
of its characteristic spectral signs, namely, two beautiful violet
Hues. Radium, too, which was discovered in 1900 and was
found to have the atomic weight 226, completely satisfied this
test and fitted exactly into the place which this number
reserved for it in the table. Thus prediction and confirmatory
discovery were fully congruent in this case ; the experiment
followed on the visionary insight just as a EucUdean proof
follows on a mathematical assertion, and we have every reason
to say that the system of Mendelejew and Lothar Meyer has
stood the crucial test. Future hypotheses will perhaps sup-
plement the system or enlarge our knowledge of it, but will
certainly not reduce it ad ahsurdum.

Apart from these cases, there are achievements by men
who may be called lucky discoverers, although they displayed
no genius for finding nor for creating. The philosopher-
physicist, Ernst Mach, has devoted a lecture to such intellects,
which seems to me very valuable, if only for the reason that he
traces back the conceptions of discovery and invention to one
common root of knowledge, and explains their difference as
being due only to a difference in the application of this
discovery.

But when Ernst Mach in this lecture, '* On the Influence
of Accidental Circumstances on the Development of Inventions
and Discoveries," extends the influence of chance to include
accidental circumstances that can only enter when the dis-
coverer is closely attentive, it seems to me that certain Umita-
tions are advisable. Otherwise, if we pursue Mach's line of

THE DISCOVERER 109

thought to its extreme, we could declare every discovery to
be due to chance, and this would be the end of the intuitive-
creative idea. This assertion would ultimately mean that
genius owes its achievements to the accidental arrangement
of the molecules in the brain-cells of its associated body. This
would be just as wrong as saying that chess is a game of chance
because we lose a game when, by chance, we come up against a
better player.

Huyghens, the great discoverer and inventor, says, in his
Dioptrica, that he would have to consider anyone who invented
the telescope without the favourable intervention of chance
to be a superhuman genius. Why should he choose just the
telescope ? To many the invention of the Differential Calculus
will appear grander and due to a higher degree of ingenuity.
And since it was produced quite methodically, and since chance
was excluded, we may follow Huyghens and with good reason
proclaim its authors sjaperhuman geniuses.

Many a true inspiration is dependent on some impulse from
without. Who discovered Electromagnetism ? The world-
echo answers, " Oersted," with the same confidence that it
couples together the names America and Columbus. This
shows how enormously important was the achievement.
Next to steam-power nothing has exerted such a revolutionary
influence in all branches as electromagnetism. Without it,
the world of to-day would present a totally different aspect.
Without it, we should have no dynamos, no electric trams, no
telegraphy, no electric-power stations, all of which are due to
the work of Arago, Gay-Lussac, Ampere, Faraday, Gramme,
and Siemens. Without it, there would be none of the abundance
of brilHant discoveries that are associated with the names of
Maxwell, Hertz, and Einstein. The fact that physics used to be
divided into three parts — Mechanics, Optics, Electrodynamics
— and that, since then, the coherent unity of the physical
picture of the world has been developed, shows us a picture in
the background of which we see the illuminating figure of Hans
Christian Oersted. It must not be overlooked, however, that
in the case of his great discovery, too, chance played a definite
part. It occurred one day when Oersted was holding a lecture
in the winter of 1819-20 ; a magnetic needle situated near

/

110 EINSTEIN THE SEARCHER

his Volta-battery began to vibrate irregularly. This appar-
ently unimportant trembling of the metal points contained the
key to a fact, the whole consequences of which could in no
conceivable way have entered the mind of this observer of a
hundred years ago, in spite of the genius of the Danish scientist,
which is documented in the classical and far-famed dissertation,
*' Experimenta circa effectum conflict us electrici in Acum
magneticara," which appeared in July 1820. It cleared the
way for intuitions that were equally as fruitful for theory as for
practice. Thirteen years after this initial discovery the world
saw the first very important consequence in Gauss' and Weber's
electric telegraph, and a little later the eminent discoverer
Fechner, in Leipzig, proclaimed it as his conviction that,
within two years, electromagnetism would entirely reform the
world of machines, and would entirely supersede steam- and
water-power. Of course, his time estimate fell far short of the
mark. It has been reserved for the present generation to
realize that we live in an electromagnetic world, and that we
have, theoretically and practically, to spend our life electro-
magnet ically. The first indication of this knowledge hung
upon the quivering point of a magnetic needle, and from it
there evolved the electromagnetic ideas that we are so fond of
picturing as our handmaids, but which, in reality, are sovereign
over us all.

A great deal of the history of discovery must be revised
and corrected. The Spiral of Archimedes is not due to
Archimedes, nor Marriotte's Law to Marriotte, nor Cardan's
formula to Cardan, nor Crookes' Tube to Crookes, and Galvan-
ism is only related to Galvani by the following anecdote. It
arose from an accidental experience of Madame Galvani in
the kitchen : a half-skinned frog that was to be fried for the
evening meal happened to rest between a scalpel and a tin plate,
which brought it into metalHc contact with an accidental
discharge of electricity ; the frog twitched ; the head of the
house gave a very naive interpretation to the phenomenon ;
and it was under such auspices that Galvanism made its entry
into the world. It would be a futile task to endeavour to trace
the connexion between experiment and the underlying idea,
which, in this case, first came to fife in Alexander Volta, What

THE DISCOVERER 111

would have remained a mere frog-dance if left to Galvani now
acquired the rank of a discovery through the work of a thinking
physicist, who set up a ** Voltaic series " ; this discovery then
assumed power and dignity in the hands of Nicholson, Davy,
Thomson, Helmholtz, and Nernst. The words Galvanic Elec-
tricity should be made to give way entirely to Voltaic
Electricity,* as in the case of many another expression fm
which chance and insufficient thought have stood sponsor.

It often happens that experiment acts as a corrective of
the underlying idea, neither confirming nor contradicting, but
nursing it, as it were, strengthening, and purging it of errors.
Such experiments, partly in conjunction with chance, play
an important, sometimes a decisive, role in the works of
Dufay, Bradley, Foucault, Fresnel, Fraunhofer, and Rontgen.
Faraday, who was incapable of observing otherwise than
intensively, found himself compelled, whilst studjdng induction
phenomena, to alter his initial view, and it is just this correction
by experiment that constitutes Faraday's real discovery. In
many cases the initial idea is corrected, nay surpassed, by te
result. Columbus worked methodically when he set out to
reach the East Indies by travelHng westwards ; but what he
discovered was not a confirmation of his nautical idea only, but
something much greater, which certainly did not lie in his
calculation. Thus he became the archetype of all searchers,
who had thought out and anticipated essentially different
conditions from those that were afterwards discovered to be
prevalent. Among these are to be counted Priestley and
Cavendish, who clung to the erroneous notion of phlogiston,
even when they had the evidence to the contrary in the ele-
ments they had themselves discovered, namely, oxygen and
hydrogen. Graham Bell, the inventor, was seeking something
quite different from what he later hit on : as a teacher of the
deaf and dumb he was trying to give a visual picture of sounds,
in order to make clear the formation of sounds to his pupils ;
this led him to construct an electrical apparatus, which finally
led to the discovery of the telephone.

The truest and sharpest contrast with the experimentum
cruets is furnished by experiment when it shows the exact

* The usual term in England is VolWc Electricity, or, simply, Current
Electricity.— H. L. B,

112 EINSTEIN THE SEARCHER

opposite of what the explorer was expecting. But since an
absolute No entails a very decisive Yes — namely, in this case,
the affirmation of a relationship that was previously held to
be impossible — a negative experiment of this kind, when it
occurs, will be followed by momentous consequences ; these
will be the more important in proportion as the question, the
affirmation of which was expected by the physicist, is of a
fundamental character.

The experiments of Michelson and Morley, directed at
proving the existence of the ether, are to be regarded as the true
classical instances of these experiments answering with an
overwhelming negative. Their first effect was to produce a
sense of helplessness, a check to thought, a void in the chamber
of ideas. And to fill this void there arose new \dews of the
world in which we nowadays recognize the true thought-
pictures of the universe. The great names — Lorentz, Min-
kowski, Albert Einstein — shone out I

As there are forerunners for almost every important event,
so also in the case of the experimentum cruets of Michelson
and Morley. Henri Poincar6, the famous mathematician,
whilst still a student of the £cole Polytechnique, had initiated
experiments with his fellow-student Fav^, which followed
the same object. The Michelson-Morley experiment was at
least a hundred times more accurate. In each case the con-
clusion was that the laws of optics are not disturbed by a
motion of translation, such as that of the earth through space
this is, however, contrary to what the old physical ideas lead
us to expect.

If we assume the existence of a space-filling ether, the
earth, owing to its own velocity of nineteen miles per second,
would have to pass through a hurricane just as in the case of
travellers sitting in an open train rushing along at very great
speed. If we send out light rays in all directions simultane-
ously from any point on the earth's surface, some will travel
in the teeth of the ether-storm, others will experience only a
part of the storm's power ; so that of two hght-rays travelling
in exactly opposite directions the retardation of the one should
be equal to the acceleration of the other ; and yet they are not
quite equal, for a simple calculation shows that in every case
the retardation is slightly more than the acceleration.

THE DISCOVERER 113

This may be made clear by means of a model of easy con-
stniction, or, better still, by considering a ship that is subject
to a constant current and, simultaneously, to a pressure of the
wind. The time taken by the boat in making a trip up and
down stream can never be the same for the cases when the
wind is in the direction of the current, and vice versa.

In the case of the ray of Hght, which is sent backwards and
forwards by means of a contrivance of mirrors, this fact should
be clearly demonstrated by means of the interference-fringes,
which are able to show much smaller effects than the experi-
ment demands. The experimental oracle was to speak, but
it remained silent. This portentous silence signified : no
interference-effect, no action of the ether-current, no influence
due to translation — nothing I

This " nothing " compelled a decision of a very startling
kind, for the result of this experiment was in direct contradic-
tion to another famous experiment. Fizeau had proved that
the ether is practically rigid and remains fixed in interstellar
space. A decision had to be taken in favour of Fizeau or
Michelson and Morley. Yet this was impossible, for both had
operated with unsurpassable accuracy. It was impossible
to reconcile both views as they were diametrically opposed.
This contradiction remains, even if we assume a different
hypothesis, not involving the ether, for Fizeau's experiment.
A solution was impossible without undertaking revolutionary
changes in the whole of physical thought.

This radical change was effected by Einstein ; and this
mysterious contradiction disappeared in the resulting revolu-
tion of thought. Einstein supplanted the absolute time-
conception by a new relative conception, and thus the perplex-
ing problem disappeared. Two great principles arose as
regulative factors in thought, and wherever these were applied,
they achieved wonders : one was the new conception of time
that deprived the earth of her unique position as the sovereign
of time by the introduction of the principle that the rate at
which time elapses is different in media moving at different
speeds ; the other is the principle oi the constancy of the
velocity of light. One feels a temptation to apply a mythical
allegory : just as the world, according to the Biblical story,
originated from nothing, so there arose from the " nothing '*
8

114 EINSTEIN THE SEARCHER

of the Michelson-Morley experiment a new world, a world of
knowledge, a cosmos of thought, in which perfect harmony
reigns.

Its truth was contained in itself before the experimental
proof was furnished. And this reahzation of truth has become
a fact in the experimentum crucis for which the sun and stars
formed the material. This will be discussed in another part
of the book.

" The really important factor is ultimately intuition,"
Einstein had said to me. It made me think of Huyghens'
remark about the genius who would have been able to create
the telescope without the help of chance. Was not this in-
tellect, imagined by Huyghens, sitting opposite me at that
moment ? An inner voice answered in the affirmative, for
Einstein's thought-complex seemed to me at that moment a
kind of telescope for the human mind, a telescope that had
arisen out of pure intuition, and whose range stretched to the
limits of the universe

CHAPTER VI
OF DIFFERENT WORLDS

Imaginary Experiment with " Lumen." — Impossibilities. — A Destroyed
Illusion. — Is the World Infinite ? — Surface Creatures and Shadow Rambles.
— What is the Beyond ? — Action at a Distance. — Ideas of Multi-dimensional
Regions. — Hypnotism. — Recollections of Zollner. — Science and Dogma. — The
Trial of Galilei.

A CONVERSATION held during April 1920 destroyed
an illusion which had become dear to me.
It concerned the fantastic figure, ** Lumen/* con-
ceived as an actual human being, imagined as endowed with
an extraordinary power of motion and keenness of sight. Mr.
Lumen is supposed to be the invention of the astronomer
Flammarion, who produced him in the retort of fancy, as Faust
produced Homimculus, to use him to prove the possibiUty of
very remarkable happenings, in particular, the reversal of
Time.

Einstein declared outright : ** Firstly, Lumen is not due
to Flammarion, who has derived him from other sources ; and
secondly. Lumen can in no way be used as a means of proving
things."

MoszKOWSKi : ** It is at least very interesting to operate
with him. Lumen is supposed to have a velocity greater than
that of light. Let us assume this as given, then the rest foUows
quite logically. If, for example, he leaves the earth on the day

of a great event, such as the battle of Waterloo, and May

I trace out this example, at the risk of tiring you ? "

Einstein : Do repeat it, and act as if you were teUing some-
thing entirely new. It is clear that the Lumen-story gives
you great amusement, so please talk quite freely. But I can-
not forgo the privilege of showing later how the whole adven-
ture and its consequences must be demoHshed.

M. : Well then, the person. Lumen, sets o£E at the end of
the battle of Waterloo to make an excursion into space with a

116

116 EINSTEIN THE SEARCHER

speed of 250,000 miles per second. He thus catches up all the
light -rays that left the field of battle and moved in his direction.
After an hour he will already have attained a lead of about
twenty minutes. This lead will be gradually increased, so that
at the end of the second day he will no longer be seeing the
end of the battle, but the beginning. What has Lumen been
seeing in the meantime ? Clearly he has been observing events
happening in the reverse direction, as in the case of a cinemato-
graph which is exhibiting pictures backwards. He saw the pro-
jectiles leaving the objects they had struck, and returning into
the mouths of the cannon. He saw the dead come to life, arise,
and arrange themselves into battahon order. He would thus
arrive at an exactly opposite view of the passing of time, for
what he observes is as much his experience as what we observe
is ours. If he had seen all the battles of history and, in fact,
all events happening in the reverse order, then in his mind
*' before " and " after " would be interchanged. That is, he
would experience time backwards ; what are causes to us
would be effects to him, and our effects would be his causes ;
antecedents and consequents would change places, and he
would arrive at a causality diametrically opposite to our
own. He would be quite as justified in adopting his view of
the happening of things, according to his experiences, and of
the causal nexus as it appears to him, as we are justified in
adopting ours.

Einstein : And the whole story is mere humbug, absurd,
and based on false premises, leading to entirely false con-
clusions.

M. : But it is only to be taken as an imaginary experiment
that plays with fantastic impossibiUties to direct our ideas on
to the relativity of time by a striking illustration. Did not
Henri Poincare adduce this extreme example to discuss the
" reversal *' of time ?

Einstein : You may rest assured that Poincar^, even if he
used this example as an entertaining digression in his lectures,
took the same view of Lumen as I do. It is not an imaginary
experiment : it is a farce, or, to express it more bluntly, it is
a mere swindle ! These experiences and topsy-turvy per-
ceptions have just as httle to do with the relativity of time,
such as it is taught by the new machanics, as have the personal

OF DIFFERENT WORLDS 117

sensations of a man, to whom time seems long or short accord-
ing as he experiences pain or pleasure, amusement or boredom.
For, in this case, at least the subjective sensation is a reality,
whereas Lumen cannot have reality because his existence is
based on nonsense. Lumen is to have a speed greater than
that of hght. This is not only an impossible, but a foolish
assumption, because the theory of relativity has shown that
the velocity of light cannot be exceeded. However great the
accelerating force may be, and for however long it may act, it
cannot cause this limit to be transcended. Lumen is supposed
to be equipped with the organ of sight, that is, he is supposed
to have a corporal existence. But the mass of a body be-
comes infinitely great when it reaches the velocity of hght, so
that it is quite absurd to go beyond this stage. It is admissible
to operate with impossibilities in imagination, that is, with
things that contradict our practical experience, but not with
absolute nonsense. That is why the other adventure of Lumen,
in which he jumps to the moon, is also an absurdity. In this,
he is supposed to leap with a speed greater than light, and,
when he reaches the moon, to turn round instantaneously,
with the result that he sees himself jumping from the moon to
the earth backwards ! This jump is logically meaningless ;
and if we try to make deductions of an optical nature from
such a nonsensical assumption, we deceive ourselves.

M. : Nevertheless, I should claim extenuating circum-
stances for this case on the ground that I am enlisting the
help of the conception of impossibiUty. A journey even at
a speed of only looo miles per second is impossible for a man
or a homunculus,

Einstein : Yes, according to our experience, if we measure
it against facts. We cannot state definitely that a journey
into the universe at an enormous yet limited velocity is abso-
lutely impossible. Within the indicated bounds every play of
thought that is argued correctly is allowable.

M, : Now, suppose that I strip Lumen of all bodily organs
and take him as being a pure creature of thought, entirety
without substance. A velocity greater than that of hght
can be imagined, even if it cannot be realized physically. If,
for example, we think of a lighthouse with a revolving Ught,
and consider a beam of light about 600 miles long, which rotates

118 EINSTEIN THE SEARCHER

200 times per second. Then we could represent to ourselves
that the light at the circumference of this beam travels with a
speed of nearly 760,000 miles per second.

Einstein : As for that, I can give you a much better ex-
ample of the same thing. We need only imagine that the
earth is poised in space, motionless, and non-rotating. This
is physically admissible. Then the most distant stars, as
judged by us, would describe their paths with almost un-
limited velocities. But this projects us right out of the
world of reality into a pure fiction of thought, which, if
followed to its conclusion, leads to the most degenerate form
of imagination, namely, to pathological individualism. It is
in these realms of thought that such perversities as the
reversal of time and causaUty occur.

M. : Dreams, too, are confined to the individual. ReaUty
constrains all human beings to exist in one and the same world,
whereas, in dreams, each one has his own world with a different
kind of causaUty. Nevertheless, dreams are a positive experi-
ence, and signify a reality for the dreamer. Even for waking
reaUty it would be easy to construct cases in which the causal re-
lationship is shattered. Suppose a person who has grown up in
a confined retreat, such as Kaspar Hauser, looks in a mirror for
the first time in his life. As he knows nothing of the pheno-
mena of optical reflexion, he sees in it a new, objective world
that gives a shock to, or even subverts, his own idea of causality
in so far as it may have become developed in him. Lumen sees
himself jump backwards, whereas Kaspar Hauser sees himself
performing gestures on the wrong side of his body ; should it
not be possible to draw a reasonable parallel between these two
cases ?

Einstein : Quite impossible. However you set about it,
your Lumen will inevitably come to grief on the conception of
time. Time, denoted in physical expressions by the symbol
" t," may, indeed, be given a negative value in these equations,
so that an event may be calculated in the reverse direction.
But then we are dealing with pure matters of calculation, and
in this case we must not allow ourselves to be drawn into
the erroneous belief that time itself may travel negatively,
that is, retrogressively . This is the root of the misapprehension :
that what is allowable and indeed necessary in calculations

OF DIFFERENT WORLDS 119

is confused with what may be thought possible in ReaUty.*
Whoever seeks to derive new knowledge from the excursions
of a creature like Lumen into space, confuses the time of an
experience with the time of the objective event ; but the
former can have a definite meaning only if it is founded on
a proper causal relation of space and time. In the above
imaginary experiment the order of the experiences in time is
the reverse of that of the events. And as far as causality is
concerned, it is a scientific conception that relates only to
events ordered in space and time, and not to experiences. In
brief, the experiments with Lumen are swindles.

M. : I must resign myself to giving up these illusions. I
must frankly confess that I do so with a certain sadness, for
such bold flights of constructive fancy exert a powerful attrac-
tion on me. At one time I was near outdoing Lumen by
assuming a Super-Lumen, who was to traverse all worlds at
once with infinite velocity. He would then be in a position to
take a survey of the whole of universal history at a single
glance. From the nearest star, Alpha Centauri, he would
see the earth as it was four years ago ; from the Pole Star, as
it was forty years ago ; and from the boundary of the Milky
Way, as it was four thousand years ago. At the same moment
he could choose a point of observation that would enable him
to see the First Crusade, the Siege of Troy, the Flood, and
also the events of the present day simultaneously.

Einstein : And this flight of thought, which, by the way,
has been indulged in repeatedly by others too, has much more
sense in it than the former one, because you may make an
abstraction which disregards speed altogether. It is only a
limiting case of reflection.

M. : I should Uke to touch on other limiting cases, in
particular two that I find it impossible to interpret. Lotze
mentions them in his Logic. The first concerns the infinitely
long lever whose fulcrum, or turning-point, is at the confines
of the universe. According to the Laws of Levers, a mass of

* Perhaps an analogy will serve to make this clear. Suppose that a certain
quantity of some foodstuff is consumed by yV head of population. The
false inference would be that a population is possible which has ^ heads!
In the same way the statistics may be quite correct in arriving at the figure i
suicides, but if we leave the realms of calculation, then the ^ suicide loses its
meaning entirely.

120 EINSTEIN THE SEARCHER

magnitude zero will suffice to keep in equilibrium at the end
of the other lever-arm any weight, no matter whether it is
a million times heavier than the earth. Our imaginations
cannot even picture this. Yet I cannot feel satisfied with the
mere explanation that it is an exceptional case, an extension
of a general law to a case in which it is no longer applicable.
The second example is still more perplexing because it does
not require a journey into other worlds, but leads us into in-
conceivable consequences even if we remain on the earth.
Lotze considers this second Umiting case easier ; to me it
seems more difficult. It is this : The force that a wedge exerts
is inversely proportional to its thickness. If it is infinitely
thin, this formula gives an infinitely great result, whereas,
actually, the force exerted is nil. This very thin wedge, trans-
formed finally into a geometrical plane, should be able to split
in twain any wooden or even steel block. And now, consider
a special arrangement of this wedge in which it is resting with
its extremely sharp edge vertically downwards, whereas at the
top it broadens to a Httle ledge which supports a weight. We
then get the incredible result that this wedge, which can be
imagined concretely, should be able to cut through the whole
earth with its extremely fine edge, if placed on some base.
Where is the fallacy in this case ?

Einstein : The mechanical facts have not been taken
sufficiently into consideration. — He illustrated his further
remarks by drawing a few strokes with his pen, and proved
from his diagram that a wedge of this sort would be able to
perform what I assumed, only if the base on which it is placed
is composed of separate laminae. Otherwise the assumption
that the force is infinitely great would be erroneous.

After this digression to a limiting case on the earth we
returned to more general problems, and the question of the
finitude or infinitude of the universe. Shortly before, Einstein
had given an address to the BerUn Academy on this point,
involving difficult calculations, and I hoped to hear from him
an easy explanation at least in general terms.

It is one of the ultimate problems. Whoever talks of the
limits of the world endeavours also to mark off the bounds
of the understanding. The average person, at first sight,

OF DIFFERENT WORLDS 121

almost always decides in favour of an infinite universe, on the
ground that a finite world is inconceivable. He argues that, if
it were considered finite, we should immediately be confronted
with the question : What lies beyond the finite boundary ?
Something must be present, even if it is only empty space.
This brings us into an inevitable conflict with the first of Kant's
" antinomies," with the thesis and antithesis, from which there
is no escape. What is the meaning of the fact that the appre-
hensive understanding seeks refuge in " Infinity " ? It signifies
that he gets entangled in the folds of a negative conception,
that furnishes him with no explanation at all, and expresses
merely that his first assumption of finitude cannot be thought
out to its conclusion.

Besides this, a second disturbing question arises. Is there
a finite or infinite number of stellar bodies ? If this question
refers to an assumed infinite space, even if such space is in-
conceivable, then there are two possible answers. For it
would be possible to imagine a finite number of stars even if
no limit could be found for space.

WherccLS the general question of space in the universe
belongs exclusively to speculative philosophy, the star-question
is not purely metaphysical, but is physical, too, and has accord-
ingly been treated by physicists. The great astronomer
Herschel imagined he could solve it by means of optical prin-
ciples, and he arrived at the conclusion that the number of
heavenly bodies must be finite, as otherwise the aspect of
the starry firmament, from the point of view of illumination,
would be entirely different. But this proof did not estabhsh
itself among scientists, for the number of stars of the type of
the sun might be finite, whilst there was an infinite number
of dark stars.

A further question presented itself : Would it be possible
for a definite part of the heavens (say, that north of the ecHptic)
to contain an infinite number of stars, whilst other parts con-
tained only a finite number ? At first this sounds very extra-
ordinary, but it is by no means unreasonable, as a concrete
example will show : If, on a scale of temperature, we count the
degrees of heat from a certain point, then they stretch ap-
parently to infinity in one direction, whereas they extend
only to — 273° (Centigrade) in the other direction, that is, to the

122 EINSTEIN THE SEARCHER

absolute zero. Thus we can imagine an arrangement which
stretches to infinity only in one direction.

To get an insight into the discussion by Einstein which is
about to follow, we must first dispose of a certain arbitrariness
of language, lying in the customary indiscriminate use of the
terms, infinite, immeasurable, and unbounded. Suppose we
have a globe about one foot in diameter, the surface of which
is inhabited by extremely small, ultramicroscopic creatures
that can move about freely and can think. The surface of the
sphere constitutes the world of the micro-men, and he has a
very good reason for considering it infinite, for, however far
and in whatever direction he may move, he never encounters
a boundary. But we, who live in our space, look on to this
spherical surface, and recognize that his judgment is erroneous.
To us his spherical world seems decidedly finite and quite
measurable, although it has no determinable beginning and no
end, and thus must appear unbounded to the micro-man. In
fact, we ourselves may regard it as boundless, if we can succeed
in forming an abstraction that leaves out of account its limita-
tions in our own space.

Now, it might occur to a particularly intelligent micro-
being to undertake a voyage for the purpose of making measure-
ments. He carefully marks his point of departure, walks
straight ahead in a certain direction, describing a circle on his
sphere — a circle which he will necessarily regard as a straight
line. He continues ever onwards in the firm conviction that
he is getting farther and farther away from his starting-point.
Suddenly, he discovers that he has reached it again. He dis-
covers, by the mark he made, that he has not been describing
a straight line, but a line that merges into itself.

The micro-professor would be compelled to declare : Our
world, the only one known to me, is not infinite, although in a
certain sense boundless. Moreover, it is not immeasurable,
since it can be measured in at least one direction by the number
of steps I have walked. From this we may infer that our former
geometrical view was either wrong or incomplete, and that, in
order to understand our world properly, we must build up a
new geometry.

We may assume that the majority of the remaining micro-
inhabitants would at first protest strongly against this decision.

OF DIFFERENT WORLDS 128

The idea that a line, which appears to them to be pointing
always in the same direction, is curved, seems to them in-
conceivable and absurd. They would only gradually overcome
their scruples of thought by getting an insight into a newly
developed geometry that makes clear to them for the first time
the conception of a sphere.

In our world of space, which includes all stars, we are the
micro-inhabitants. We have been born with, or have in-
herited, the idea of a straight and ever-advancing path in
space, and we become filled with the utmost astonishment if
some one asks us to believe that if we undertake a voyage in
one direction out into the universe, beyond Sirius and a million
times farther, we should finally arrive at our starting-point
again, although we had not changed our direction. But the
macro-being, who belongs to a universe of higher dimensions
and who looks on our world as we looked on the above spherical
world one foot in diameter, sees the narrowness of our view.
We, too, are in a position to rise above this narrow view by
means of a theory founded on our experience, which will lead
us to an extended world-geometry, just as the micro-professor
used his experience to extend his theory of the circle to include
the conception of a sphere.

After these preHminary remarks we shall endeavour to get
an insight into Einstein's reasoning, not in the form in which
it was originally presented (in the Report of the Proceedings of
the Berlin Academy of Science of 8th February 1917), but in a
very easy description which was given to me during a conversa-
tion. Here, too, I shall try to preserve the sense of Einstein's
remarks without binding myself strictly to his words. For
although I am indebted to him for his efforts to avoid difiicult
points, yet the aim of this book is, if possible, to make the
explanation still easier. Any lack of accuracy arising from
this last simpUfication is to be debited to me. The new form
of representing the argument, which is as important as it is
fascinating, is, of course, due to Einstein.

The final result stated by Einstein was : The universe, both
as regards extent and mass, has finite limits and can be
measured. If anyone asks whether this can be pictured, I shall
not deprive him of the hope. All that is required is a power
of imagination that is great enough to follow a pictorial de-

124 EINSTEIN THE SEARCHER

scription and that can take up the right attitude towards a sort
of figurative representation.

Let us again imagine a sphere of modest dimensions with
its two-dimensional surface. We are concerned only ^\ith
the latter, and not with the cubical content. The sphere is to
be considered as resting on an absolutely plane white table of
unlimited extent in all directions. The sphere touches the
table at a single point which we shall call its South Pole ;
on the top side directly opposite, we have the North Pole.
To simphfy matters we may make a sketch on paper of a
vertical section through the centre of the sphere. This profile-
picture will show us the sphere as a circle, and the white
table as a straight line ; the line joining the two poles is the
axis of the globe, and the sectional circle is a meridian.

Let us further suppose a creature (resembling, say, a lady-
bird in shape) having length and breadth, but no thickness, to
crawl along this meridian. Although it has no thickness, we
shall imagine it to have one property of a solid body, that of
being opaque, so that it can throw a shadow if properly illu-
minated. We assume the globe itself to be transparent.
At the North Pole we suppose a very strong point-source of
light, a little electric lamp, that sends out rays freely in aU
directions.

The insect begins its journey at the South Pole and sets
out along the meridian to reach the North Pole. It is illu-
minated by the lamp all the way, so that it continually throws
a shadow on the white table. The shadow moves along the
table farther and farther from the South Pole, in proportion
as the insect moves up the meridian, with the difference that
while the insect is describing an arc of a circle, its shadow
moves along a straight line. The position of the shadow can
be determined at any moment by drawing the straight line
connecting the lamp to the insect, and producing it to meet
the white surface of the table ; the point of intersection is the
projection of the insect on the plane.

At the beginning of the excursion the shadow is exactly as
large as the flat insect itself, if we assume that its dimensions
are negligible compared with the surface of the sphere, for
it will then coincide with its own shadow. But when the insect
crawls upwards, its shadow will increase, because of the

OF DIFFERENT WORLDS 125

shortened distance between the insect and the lamp, and because
the points of projection on the table separate more and more
as their distances from their corresponding points on the sphere
become greater. There is thus a twofold increase. The
shadows move away more and more rapidly, and at the same
time increase in size.

When the insect gets very near the North Pole, its shadow,
now of enormous dimensions, has moved to a very great dis- \
tance ; and when finally it reaches the Pole, its shadow
becomes infinitely great and thus stretches to infinity.

But let the insect wander on along the meridian, past the
North Pole, down towards the South. At the moment when it
passes the upper Pole its shadow jumps from the right side to
the left. Its shadow now emerges from an infinite distance to
the left, and, instead of being infinite size, again becomes finite
in dimensions as it approaches. It contracts as it approaches,
and, in short, the same process as occurred during the first
half of the journey now occurs in the reverse order.

[If we fix on the critical moment of the jump from the right
to the left, that is, from plus infinity to minus infinity, we may
encounter difficulties. For the surface-creature pursues its
way without interruption and continuously, and we experience
a wish to ascribe to it a shadow-path that is also unbroken and
continuous. This is possible only if we assume the two points
at infinity to be connected, that is, if we consider them identi-
cal. This assumption will seem more natural if we reason as
follows. In the profile-picture the table is represented as a
straight line, and it is along this line that the shadow travels.
We may regard this line as an infinitely great circle, for an
infinitely great circle has zero curvature, just as the straight
line, from which it is therefore indistinguishable. The in-
finitely great circle has, however, only one point situated at an
infinite distance, that is, it associates together the two apparent
points at infinity of the straight line with which we identify
it. Accordingly, we preserve the continuity of the shadow-
journey, too. Einstein considers it allowable to say that the
right and the left portion each represent a half of the infinite
projection, which becomes complete only when the two ends
are joined.]

Now we must be prepared for an effort of thought which

126 EINSTEIN THE SEARCHER

will need considerable help from our imaginations. Firstly,
instead of one surface-creature, we shall suppose several crawl-
ing about on different meridians, so that a series of shadows
will be moving about along straight hues radiating from the
South Pole. Next, let us imagine the whole picture to have
its dimensions increased by one, that is, we transform the
plane-picture into a space model. The phenomena are to
remain the same, except that they are to be strengthened by
one dimension, surface conditions becoming space conditions,
and surfaces becoming sohds.

What we now see are actual insects with round bodies (if
we retain our original type of creatures), or, since there is no
restriction as to their size — the shadows have assumed all
possible sizes — we may assume any soUd bodies whatsoever,
stars or even star-systems. Their motions take place in ex-
actly the same way as those of the shadows previously thrown
by the flat bodies.

This means that, if a stellar body moves, its size increases
until it reaches the spherical boundary of space, where it
becomes infinitely great, and, at the same moment, passes
from plus infinity to minus infinity, that is, it enters the uni-
verse from the opposite direction ; then, if it continues moving
in its original direction (as it has been doing all along), it
gradually becomes smaller in size until, finally, it reaches its
original position and its original size. If we suppose the body
to be endowed with the power of sensation, it would not be
able to observe its own changes of size, since all its scale-
measures would be altered in the same proportion. This
whole complex of phenomena would still be taking place in an
infinite world of space, but, according to the General Theory
of Relativity, the geometry that is vaHd in this world would
no longer be that of Euclid ; it is replaced by a system of
laws that arise from physics as a geometric necessity. In this
new geometry, a circle described with unit radius is a Httle
smaller than it would be in EucUdean geometry, with the
result that the greatest conceivable circle in this world cannot
assume an infinite size.

Thus we have to imagine that our solid bodies, say stars,
arrive at a point in their travels which we may term only
" enormously distant." If we call the directions right and

OF DIFFERENT WORLDS 127

left instead of positive and negative, then the process reduces
itself to this : the moving body reaches the point, which is
enormously distant on the right, and which is identical with
the point enormously distant on the left ; this means that
the body never moves out of the space continuum of this
world, but returns to its initial point of departure even when
it moves ever onward in what is apparently a straight line.
It moves in a " warped " space.

Einstein has succeeded in finding an approximate value
for this non-infinite universe, from the fact that there is a
determinable gravitational constant. In the constitution of
the universe it denotes the same for the mass-relationships of
the earth as the gravitational constant of the earth denotes for
us, namely, the quantity from which we can calculate the final
velocity attained by a freely falUng body during a unit of
time. He also assumes a probable average for the density of
distribution of matter in the universe, by supposing that it is
about the same as that of the Milky Way. On this basis
Einstein has arrived at the following result by calculation :

The whole universe has a diameter of loo million light-
years, in round numbers. That amounts to about 700 trillion
miles.

M. : Does this follow from the discussion you entered on
just now ?

Einstein : It follows from the mathematical calcula-
tions which I presented in " Cosmological Considerations arising
from the General Theory of Relativity," in which the figure I
have just quoted is not given. The exact figure is a minor
question. What is important is to recognize that the universe
may be regarded as a closed continuum as far as distance-
measurements are concerned. Another point, too, must not
be forgotten. If, in deference to your wish, I used an easy
illustration, this must not be regarded otherwise than as an
improvised bridge to assist the imagination.

M. : Nevertheless, it will be very welcome to many, who
are unable to grasp the difficult Cosmological Considerations.
The number that you mention is overwhelming in the extreme.
Indeed, it seems to me that a diameter of 100 milUon light-
years suggests an infinitely great distance more than the word
" infinity " itself, mentioned per definitionem, which conveys

128 EINSTEIN THE SEARCHER

nothing to the ordinary mind. It calls up a regular carnival
of numbers, particularly in those to whom the immense number
alone gives a certain pleasure. But you were going to give me
the number expressing the mass, too ? "

And then I learned that the weight of the whole universe,
expressed in grammes, was lo multiphed by itself 54 times,
that is 10^* (453 grammes = I lb., roughly). This seems
rather disappointing at first, but assumes a different aspect
when we represent to ourselves what this figure signifies. It
means that the weight of the universe in kilogrammes is high
in the octillions. The earth itself weighs six quadrillion kilo-
grammes, hence the weight of the Einstein universe bears
the same relation to the weight of the whole earth as the latter
bears to a kilogramme. Again, the earth's weight to that of
the sun is as i is to 324,000. Hence we should have to take at
least a trillion, that is, a milliard times a milUard, suns to get
the weight of the universe. And as far as the linear extent is
concerned, let us consider the most distant stars of the Milky
Way, which are at an inconceivable distance, expressible only
in light-years. If we place 10,000 such Milky Ways end to
end we shall arrive at this diameter of the universe, which,
accordingly, will have a cubical content a thousand milliard
times greater than the region accessible to astronomical
observation.

Thus we have a very spacious universe. Yet it is not
spacious enough to satisfy all the demands that a mathe-
matician interested in permutations and combinations might
make. One of such combinations is exemplified in the so-
called Universal Book, that originated in an imaginary
experiment of Leibniz. If we picture to ourselves the sum-
total of all books that can be printed by making all possible
arrangements and successions of our letters, each book differ-
ing from any other even if only in one symbol, then, together,
they must contain all that can be expressed in sense and non-
sense, and everything that is ever reaHzable actually or in
dreams. Hence, among other things, they would include all
world-history, all hterature, and all science, even from the
beginning of the world to the end. If we agree to the con-
vention of operating with 100 different printed signs (letters,
figures, stops, spacings, etc.), and of allowing each such book a

OF DIFFERENT WORLDS 129

million paces for signs, so that each book will still be of a handy
size, then the number of these books would amount to exactly
10 to the two-millionth power, or, in figures, i.e. lo^'OoO'Ooo.

This fully exhaustive universal library containing all
wisdom would consist of so many volumes that it could not be
contained in a case of the size of the entire stellar universe.
And, unhappily, it must be added that the closed universe,
just described by Einstein and having a diameter of a hundred
milHon Ught -years would be much too small to contain this
library.

" Nevertheless," said I, " your universe pictures something
inconceivably great ; one might call it an infinity expressed
in figures. For in your world there still remains one property
of infinity, namely, that it imposes no limitations on motion of
any kind. On the other hand, the figures proclaim a hmited
measure in the mathematical sense, however great this measure
may be. This calls up the old restlessness of mind, due to
the persistent question : What lies beyond ? The absolute
Nothing ? Or is it a something which yet does not occupy
space ? Descartes and many other great thinkers have never
overcome this difiiculty, and have always afiirmed that a
closed world is impossible. How, then, is the average person
to reconcile himself with the dimensions you have estab-
lished ? "

Einstein gave an answer which, it seemed to me, offered a
last escape to apprehensive minds. *' It is possible," so he
said, " that other universes exist independently of our own."

That is to say, it will never be possible to trace a connexion
between them. Even after an eternity of observation, calcula-
tion, and theoretical investigation, no glimpse or knowledge
of any of these ultra-worlds will ever enter our consciousness.
" Imagine human creatures to be two-dimensional surface-
creatures," he added, *' and that they live on a plane of in-
definite extent. Suppose that they have organs, instruments,
and mental attitude adapted strictly to this two-dimensional
existence. Then, at most, they would be able to find out all
the phenomena and relationships that objectify themselves in
this plane. They would then have an absolutely perfect science
of two dimensions, the fullest knowledge of their cosmos.
Independent of this, there might be another cosmic plane with
9

130 EINSTEIN THE SEARCHER

other phenomena and relationships, that is, a second analogous
universe. There would then be no means of constructing a
connexion between these two worlds, or even of suspecting
such a connexion. We are in just the same position as these
plane-inhabitants except that we have one dimension more.
It is possible, in fact, to a certain degree probable, that we
shall by means of astronomy discover new worlds far beyond
the limits of the region so far investigated, but no discovery
can ever lead us beyond the continuum described above, just
as Uttle as a discoverer of the plane-world would ever succeed
in making discoveries beyond his own world. Thus we must
reckon with the finitude of our universe, and the question of
regions beyond it can be discussed no further, for it leads
only to imaginary possibilities for which science has not the
slightest use."

Einstein left me for a while to the tumult of ideas that he
had roused up in me. After I had overcome the first shock, I
sought to gain a haven in the idea that arose out of the first
shadow-argument, in which the spherical bodies occurred that
seek to escape towards infinity on the right but reappear, in-
stead, at enormous distances on the left. Has anyone ever had
presentiments of this kind of world ? Perhaps something of
the sort is to be found in earlier books of science ? If so, they
have escaped my notice. Yet, a passage of a poet occurs to
me. It is to be found in a volume by Heinrich von Kleist ;
it is a volume dealing only with earthly matter and bare of
astronomical ideas. Imagine a book the subject of which
is a puppet-show, containing, in the middle of it, a section
foreshadowing Einstein's universe 1 Quite by chance Kleist
comes to speak of " the intersection of two fines which, after
passing through infinity, suddenly appear on the other side,
Hke a picture in a concave mirror, which moves away to infinity
and suddenly returns again and is quite close,*' and, quite in
accordance with our new cosmology, he declares : " Paradise
is locked and barred, and the cherub is behind us ; we must
make a voyage round the world, and see whether we cannot
discover an exit elsewhere at the other end perhaps."

Perhaps poets of the future will busy themselves with this
imi verse, not lyrical poets, but descendants of Hesiod, Lucretius,

OF DIFFERENT WORLDS 131

or Riickert. They will express in verse that Einstein's world
offers a source of consolation to tormented spirits which have
sickened of Kant's antinomies. For in this still almost im-
measurable world the fateful conception " infinite " has been
made bearable for the first time. In a certain way it relieves
us from what is quite inconceivable, yet into which we are
usually driven, and forms a bridge between the thesis " finite *'
and the antithesis infinite. We are brought to a common
stream, in which both conceptions peacefully flow together.
There was no mention of this in our talk, and I had good reason
for being cautious about following out the theme along these
lines. I must not allow any doubts to arise on this point :
Einstein, himself, clings with unerring logic to the strict
mathematically defined conception of infinity, and allows
no compromise with the non-infinite.

When I, on some previous occasion, sought to lead him on
to a compromise, involving a transition-boundary, it availed
me nothing that I quoted Helmholtz to support the possibility
of such an operation : my effort came to an abrupt end.

In pursuing these considerations about the universe, we
arrived at things which, in ordinary language, are usually called
" occult." In connexion with this, these remarks ensued :
" I am, of course, far from trying to trace out a connexion
between the four-dimensionality that you establish. Professor,
and the four-dimensionality of certain spiritistic pseudo-
philosophers, yet it suggests itself to me that in such occult
circles efforts will be made to derive advantage from the fact
that the same word is used in both cases. This is more than a
conjecture, indeed, for there are no misgivings among the
ignorant, and so we actually find the name Einstein quoted in
connexion with mediumistic experiments that are flavoured
with four-dimensionality."

" It will not be expected of me," said Einstein, " to enter
into discussion with ignoramuses and misinterpreters. Dis-
carding them, then, let us confine ourselves to a brief con-
sideration of the conception ' occult,' as this has played a part
in serious science. The chief example of this in history is
gravitation. Huyghens and Leibniz refused to accept gravita-
tion, for, so they said, according to Newton's view, it is an

132 EINSTEIN THE SEARCHER

action at a distance and hence belongs to the realm of the
occult. Like everything occult, it contradicts the causal
order in Nature. We must not regard Huyghens' and Leib-
niz's contradiction as being due to lack of perspicacity ; rather,
they objected on grounds which, as investigators, they had
every right to uphold. For, as far as our everyday experience
is concerned, every mutual influence of things in Nature occurs
only by direct contact, as by pressure or impact, or by chemical
action, as when a flame is lit. The fact that sound and Hght
apparently form exceptions is not usually felt as a contradiction
to the postulate of contact. The case of a magnet appears
much more striking because its effect asserts itself as a direct
manifestation of force. I must mention that when I, as a child,
made my first acquaintance with a compass — and this was
before I had ever seen a magnet — ^it created a sensation in me,
which I consider to have been a dominant factor in my Ufe up
to the very present. There is, indeed, a fundamental difference
between pressure and impact on the one hand, and what we
hear and see on the other, even in everyday experience. In
the case of light and sound, something must be ' happening '
continually, if the effect is to occur and continue. ..."

*' Yet another difference seems to enter here," I interposed.
" Is it possible to give a full explanation of gravitation by using
only the conceptions pressure and impact ? Perhaps ' pressure
at a distance * would not have seemed to contemporaries of
Newton as uninteUigible as a ' tension or pull at a distance.'
It seems to me that it is particularly difficult to imagine a pull
or an attraction towards a distant object."

Einstein does not consider this difference considerable, and
regards it as possible to overcome it even in a manner which
can be directly pictured. ** If the force is exerted by a corpus-
cular transmission," he explained, " we may imagine a * force-
shadow ' into which the bombarding corpuscles cannot pene-
trate. Thus if an obstacle, which produces such a shadow,
becomes interposed between a body A and a body B, then there
will be a lesser pressure on the side of B facing A, and hence
B will experience a greater corpuscular pressure on the other
side, with the result that B will be forced in the^direction of A,
and the observer would gain the impression of a pull from B
to A. Nowadays, when the theory of ' fields of force * domin-

OF DIFFERENT WORLDS 183

ates our physical views, we need trouble just as little about
using corpuscular pressures and impacts as about the vortices
which Descartes once considered as the ultimate causes of the
motions of the heavenly bodies. The efforts of certain
reformers to reintroduce these vortices and whirlpools as
explanations must be regarded as futile/'

" Nevertheless/' I answered, " it seems admissible to say
that, ultimately, there is always an occult element in every
physical explanation, an absolutely final and elementary
something which we recognize as a principle, without conceahng
from ourselves that we have reached the Hmit of explanation,
and our knowledge avails no further. This brings me to
another question the discussion of which, as I clearly perceive,
leads us on to dangerous ground."

Einstein : Don't hesitate to say what is troubling you.
I cannot yet see what you are aiming at.

M. : I am referring to certain phenomena which are also
called " occult " — with the object of discrediting them. They
may at times degenerate to hocus-pocus and fall into the cate-
gory of dubious arts. It seems to me, however, that scientists
have not always drawn the line with sufficient care, and that
they have been disposed to reject as humbug, without examina-
tion, everything inexplicable that dares to present itself in the
form of open display.

Einstein : In general, they will be in the right, for investi-
gators cannot be expected to occupy themselves with things
bolstered up by advertisement, and which are supposed to be
connected with some fabulous, occult regions.

M. : Nevertheless, in my opinion even among such displays
there sometimes occur phenomena which scientists should not
pass over with contempt. I, myself, have experienced such
cases, and have said to myself : There are stranger happenings
here

Einstein : — ^than are dreamt of in your philosophy, you
were about to say ?

M. : Exactly. These are things that in the guise of sensa-
tionalism often hide a physical truth well worthy of study.

Einstein : But you must not overlook the fact that in such
cases you have mostly played the part of an onlooker, and hence
were exposed to all possible manner of deception. You are

134 EINSTEIN THE SEARCHER

baffled on all sides by undiscoverable tricks and by other
persons, whose collusion you do not suspect. This renders
an objective criticism impossible.

M. : This presumes that the performing artist is not entirely
isolated. It is possible to bring about conditions that posi-
tively eliminate all tricks from the very outset.

EiNSTi-iN : If you have experienced any such cases, relate
them by all means.

M. : I shall be brief, and shall state only facts. . . .

Einstein : Or, expressed more accurately, only things
which seem to have been facts as far as you can trust to memory.
Well then, you think that you have grounds for saying that
you caught a gUmpse of a mysterious world at that time.

M. : It is certainly long ago, more than thirty years.
Hansen, the freak, one of the most eminent of his profession,
was showing hypnotic and telepathic experiments that were
partly identical with experiments that the celebrated scientist
Charcot at Paris was performing for purposes of pathology.

Einstein : Weil, then, why did you hesitate before ? These
experiments come under the head of science, and require no
occult veil to appear in the open.

M. : This touches the main issue. Hansen did not work
in the interests of science, but wished, above all, to earn money.
Nevertheless he had in his own way produced marvellous
results that were used later for scientific work. Unfortun-
ately in his case, owing to the fact that he cloaked it in occultism
at the outset, he was brusquely repudiated by scientists. The
result was that Hansen was condemned to a long period of
imprisonment in Dresden, thanks to the recommendation of
scientists who declared that the experiments were only possible
if deception was practised, and hence that Hansen was an
impostor who should be made harmless by being incarcerated.

Einstein : And how did you yourself seek to discover
whether his experiments were genuine ?

M. : Very easily and with absolute certainty. One of my
acquaintances, the wealthy race-horse owner, von Oelschlager,
had induced him by means of a high fee to experiment at his
country house, at some distance from BerHn, in the presence
of persons, not one of whom Hansen knew, and in the case of
whom there could be no question of secret collaboration. I can

OF DIFFERENT WORLDS 185

assure you that everything succeeded without exception. A
single second was sufficient for him to communicate his will
to each subject of experiment. He operated like a super-
natural being on those present.

Einstein : I should Hke to hear examples.

M. : Herr von Oelschlager introduced four jockeys, and
suggested a race in the great salon. Hansen placed them
astride over chairs, hypnotized them on the spot, described
the shape of the course, giving distances in kilometres, curves,
and even the value of the prizes. He then gave the signal
for starting. The jockeys immediately began treating their
chairs as race-horses, exhibiting all the signs of extreme
strain which accompany the actual ride.

Einstein : This is not yet a positive proof. The subjects
of experiment may have become cognizant of the fact that
they were to serve some eccentric display. Their acquiescence
in a prescribed part need by no means signify that they were
subjectively convinced of the genuineness of the affair.

M. : There could be not the slightest doubt on this point.
After a few seconds perspiration was streaming over their
faces as a result of the exertion, a symptom that exhibits
itself only when the participants are convinced of the absolute
earnestness of their undertaking. All that gazed on this
baffling ride made the acquaintance of a grotesque reahty,
and were looking into a strange world of dreams, which trans-
formed wooden chairs into Hving thoroughbreds. In the
course of his following experiments in the transference of his
will-power, Hansen experimented with an actress who was
famous at that time, and with whom he had no more acquaint-
ance than with the others. He again produced deep hypnosis,
and gave the order : I shall ask you various questions, all of
which you will be able to answer correctly, with one exception :
you will have forgotten your name. And so it happened.
In her trance the actress gave correct answers, until, when
the question, " What is your name ? " was asked, her own
name, Helene Odilon, had vanished from her memory. And
immediately afterwards, she told me herself that, in spite of
her state of coma, she had retained full consciousness, had
understood everything, and had been possessed of her memory
until it came to the critical moment when, in spite of extreme

136 EINSTEIN THE SEARCHER

efforts, she could not recollect the words Helene Odilon.
But Hansen did not stop at dictating his thoughts to others,
he also transformed corporate things. By a single motion
of his hand he converted a stable-boy into a rigid block,
devoid of sensation. Never would I have thought such an
intense state of cramp possible. He placed the boy with
his feet and head alone resting on two supports, so that the
body itself was poised in space. He then stood on the body
with his whole weight, without the rigid body of the boy
bending e\ en an inch.

Einstein : How did he, in all these cases, restore the
normal state ?

M. : Always by a single gesture, which, like everything
that he did, worked at lightning speed. I must admit that
his display became a little monotonous after a while, and
that his programme did not seem capable of much variation.
Things were different, however, in the case of a man who,
some years previously, had toured the world as an exponent
of occult phenomena, and to whom scientists will some time
in the future look back with regret. When he appeared,
most academicians took only sufficient notice of him to reject
him without having given him a trial. It was Henry Slade,
the American, who is not to be confused with other Blades
who appropriated his name in order to dupe people whose
insatiable curiosity was aroused.

Einstein : One might almost suppose that your genuine
Henry Slade served as a model for them.

M. : For certain reasons I regard this as out of the question,
mainly because the true Slade gave " demonstrations " only
occasionally, his chief object being to interest scientists. He,
himself, repeatedly asserted that he did not understand his
own achievements, and he unceasingly requested the super-
vision of professional physicists and physiologists, to whom
the unusual phases in his nature were to serve as objects of
study. The result was that people like Dubois-Reymond,
Helmholtz, and Virchow refused to see him, not to mention
experiment with him.

Einstein : These men cannot be reproached for acting in
this way. Slade was regarded as a representative of a four-
dimensioned world in the spiritistic sense ; serious scientists

OF DIFFERENT WORLDS 187

must avoid all humbug of this sort, since even sHght interest
in it can easily be misinterpreted by the ignorant pubHc.

M. : Not every one was afraid of compromising himself.
After closed doors had greeted Slade in BerHn, he went to
Leipzig, where he became an object of study for one important
scientist.

Einstein : You are referring to Friedrich Zollner, who
undoubtedly had a reputation as an astrophysicist to preserve.
But he would have served his reputation better if he had not
entered into this adventure with the American spiritist.

M. : Perhaps there will some day be cause for a revision
of opinion on this point. The documents are extant, even if,
half forgotten, they are reposing in various libraries. A
renewed investigation of Zollner's Scientific Dissertations ,
dating from 1878 to 1891, might lead to the judgment that
his ghostly interpretations are to be regarded as occult in
the worst sense, and yet one would marvel that a great scientist,
such as he was, should have felt himself at a complete loss
with his knowledge, so that he was forced to resort to abstruse
methods in order to escape from the mental confusion into
which Slade had plunged him.

Einstein : That merely shows that Slade, as a cunning
practician, surpassed him, and that Zollner did not succeed
in seeing through his machinations.

M. : This would lead one to assume that Slade knew more
physics than the Leipzig professor. For in a great number of
experiments Zollner himself had prescribed the conditions,
including all contrivances which made deception so much
the more unlikely, since Slade himself could not know what
Zollner' s intentions were. It was a question of Electricity,
Magnetism, Optics including prepared conditions of polariza-
tion, involved Mechanics, in short, things that Zollner as
a professional physicist understood thoroughly, and which,
moreover, were controlled by others of his profession. Among
the latter was the celebrated professor of Electricity, Wilhelm
Weber, who, Uke Zollner, found himself faced by phenomena
that were utterly incomprehensible to him. It would be a
profitable undertaking to bring these dissertations to light
again, and it would easily be recognized that the things de-
scribed actually deal with scientific problems and have not

138 EINSTEIN THE SEARCHER

the remotest connexion with tricks of magic. For example,
there is an account of an incredible anatomical feat. On
flour which had been placed carefully in a dish beforehand,
there suddenly appeared the imprint of a naked human foot,
whilst Slade was present at a certain distance, being fully
clothed and subject to careful scrutiny. The footprint
showed all the surface-details of the skin, as was confirmed by
authorities, just as only a left foot could produce them, but
not an artificial copy.

EiNSTEiN : And from this Zollner inferred the intervention
of supernatural beings ? He would have done better to
measure the dimensions of the foot.

M. : So he did — at once. A difference of four centimetres
between the length of Slade 's foot and the copy was disclosed.
This riddle, like so many others, remained unexplained. I
must repeat that I am not in the slightest degree disposed
to assert that occult phenomena really occur, but am interested
only in seeing that they are investigated carefully by quahfied
persons.

Einstein : Your remarks show that Leipzig scientists
did so at that time with no better result than that Zollner's
mental confusion became still greater.

M. : The conjecture remains that the Leipzig experiments,
abundant as they were, did not suffice. Allow me to ask a
direct question. Professor. Supposing another such agent of
miracles should appear, would you yourself feel impelled to
test him experimentally ?

Einstein : Your question is misdirected. I explained
above that I share the point of view taken up by Dubois-
Reymond and his colleagues.

M. : The following case may be conceived. A certain man,
X, might suddenly appear, who has control of a certain
natural force that has never before been investigated ; like
one who knew how to use electricity at a time when people
had never experienced any electrical phenomenon. He
would be able to give hundreds of demonstrations, all of which
we should relegate to the realm of inexplicable magic. We
should, for instance, be much astonished if he were to draw
sparks from a Hving person. Now, suppose two professors
express an opinion. Professor A declares the whole thing to

OF DIFFERENT WORLDS 189

be a farce, and refuses to look into it at all. Professor B is
ready to investigate the achievements of X only if the latter
subjects himself from the beginning to all the physical condi-
tions that are to be determined beforehand. And suppose the
professor arranges his conditions so that they make impossible
the occurrence of electrical phenomena. If, now, all scientists
were to behave like A and B, the consequences would be very
depressing. For here was an important field of investigation,
which is cut off owing to the distrust or obstinacy of scientists,
who should have been the first to open it up. It is quite
irrelevant whether X had the character of a charlatan or not,
for behind his charlatanism there were facts which clamoured
for investigation.

Einstein : The most that I can grant is that your imagined
case does not lie outside the scope of possibility. Yet the
chance that there is such a " natural force " hitherto undis-
covered by Man, that is, one that is a " secret force " as far as
we are concerned, is so vanishingly small that it may be set
down as equal to impossible. I should refuse to take part in
any such practices, served up in the form of sensation, for one
reason that I should regret the waste of time, as there are
better things to do. It is a different matter if the mood takes
me to visit a variety entertainment, in order to derive amuse-
ment from such mystifications. For example, only yesterday
I was in a little theatre, in which, among diverse items, a
thought-reading woman was performing. She correctly guessed
the numbers 6i and 59 that I had in my mind. But let no
one mention this as a case of telepathic actions at a distance
or wireless communication between minds, for an intermediate
person, the manager, was present, and I had to whisper the
numbers to him. The distance to the stage was certainly
too great to allow the sound to be conveyed directly to an
audible degree. Hence there must have been a different, very
cunningly arranged code of signals, which eluded the notice
of people in the stalls. The process consists actually in an
extraordinary refinement of observation, which does not,
however, seem to me any more wonderful than the training
of a reckoner who extracts cubic roots mentally, or than the
practised muscles of a juggler all working in unison to enable
him to perform feats with twelve plates simultaneously.

140 EINSTEIN THE SEARCHER

M. : It gives me enough satisfaction, Professor, that you
conceded me before a certain limited chance of finding a last
refuge in occultism. And even if you, yourself, as a representa-
tive of the most rigorous research of physical reahty, refuse to
consider it, yet the fact that many others are drawn irresistibly
towards mysterious phenomena cannot be denied. Should
one feel shame on this account ? I beheve that, in this matter,
we are touching on inner confessions that are quite independent
of the standard of the mind in which they are embedded.
Newton considered the key of the universe to be a personal
God, whereas Laplace proclaimed : Dieu — je n' avals pas besoin
de cette hypothese : this contrast allows no inference to be drawn
as to their relative keenness of mind. And probably the same
may be said of the question whether there are other hidden
universes besides the one in which we live. In any case, those
who feel enthusiasm for such questions can quote in their sup-
port good names from the learned world. Immanuel Kant
occupied himself seriously and intensively with the wonders of
Swedenborg, Kepler practised Astrology, in which he had a
firm belief, Roger Bacon, Cardanus, Agrippa, Nostradamus,
van Helmont, Pascal, and, among the modern, Fechner,
Wallace, Crookes, are to be counted among the mystics. No
matter whether the views they held were theosophical, occult,
four-dimensional in the spiritistic sense, or coloured by any
other superstition ; they proclaimed that things that could
be rigorously proved were, alone, insufficient for them. Out of
presentiment and conjecture they constructed wings with which
to fly into regions extra naturam. This is how it happened that,
as the common folk could not find a place in science for many
extraordinary achievements, they assigned their authors to the
realm of magicians, as in the case of Paracelsus, Albertus
Magnus, Raimundus LuUus, Sylvester II, who were regarded
as sorcerers. And this coin is still current : to Edison, of
our times, the term, " sorcerer of Menlo-Park," has become
attached. In the minds of the populace discovery and in-
vention, works of genius and supernatural phenomena, become
confused and indistinguishable ; it may even happen to you.
Professor, that your works will become invested with legend.
I should not Hke to conjure up what your fate would have been
if your theory of relativity had originated at the time of the

OF DIFFERENT WORLDS 141

Inquisition. For the views put forward by Giordano Bruno
are mere child's play compared with your theory of the universe
as a quasi-spherical closed space of hyper-Euclidean character.
The tribunal of the Inquisition would not have understood
your differential equation, gravitational potentials, tensors,
and equivalence theory ; they would abruptly have declared
the whole theory to be a magical formula or a manifestation
of the devil, and would have honoured it and you with a
funeral pyre.

Einstein : This is clearly a slight exaggeration. Mathe-
matico-physical and astronomical works have never been
attacked by the Papal courts, but, on the contrary, have been
much encouraged by them down to the present day. This is
abundantly clear from the fact that we can set up a whole list
of Brothers of Orders, particularly Jesuits, who have made
eminent discoveries in natural science. From my personal
knowledge of you, I foresee that you will one day sketch a
fantastic trial, in which the new world-system will have to
defend itself against the Sanctum Officium.

M. : This would be a very grateful task, judged from the
literary point of view. What a splendid colouring could be
obtained by bringing these two worlds of thought into conflict
with one another, the Relative against the Absolute, which has
been estabUshed in tradition and dogma. But we need not
even call the historical fancy into action, for, actually, the
theory of the structure of the world is even now still at variance
with traditional ideas, that act with dogmatic violence. There
is no need to deny the fact that every person of education, who
makes the acquaintance of Lorentz's, Minkowski's, Einstein's
ideas for the first time, feels excited to offer contradictions, and
becomes involved in a tumult of pros and cons, and each one ex-
periences in himself the excitement of an inquisitorial tribunal.
The triumph of the new theory passes over the corpses of con-
ceptions that lie at the cross-roads of thought and, long after,
retain a ghostly existence. Only very few of us are aware of
the further inner revolution that awaits us along the line of
development of Einsteinian ideas ; we have only vague pre-
sentiments that whisper to us that the end of forms of thought
once considered as irrefragable is drawing nigh. When once
the principle of causality has been set on a relative base, and all

142 EINSTEIN THE SEARCHER

" properties " have been resolved Into occurrence, and all that
is three-dimensional has come to be recognized as an abstraction
from the four-dimensional world that is alone valid, then the
time will have come to arrange for the death procession of all
the philosophies that once served as the main pillars of thought.

A retrospect of the trials of Giordano Bruno and of Galileo
GaUlei offers certain parallels other than those usually discovered
by scholars. And if, to-day, we proclaim Einstein as the Galilei
of the twentieth century, it must be added that in character he
is fortunately a Bruno and not a Galilei. For it is not true
that the latter came out of the persecution as a moral victor
with an eppur si muove, rather, in spite of the protection of
influential prelates and dignitaries, even of the entourage of
the Pope, he lacked courage and bowed his head, betraying
his science and denying himself as well as Copernicus. Are
we to picture how Einstein would have acted under similar
circumstances, even if they cannot recur again ?

Whoever has even an inkling of his character will entertain
no doubts. At that time, three hundred years ago, the materials
for a magnificent scene, " one world versus the other,'* lay ready.
Only one condition was wanting, the moral courage of the hero.
The lack of this one factor spoilt the final act for the history of
that time. The fine ethical feelings of later generations have
had to be propitiated by improvising a legend iridescent with
beautiful colours.

CHAPTER VII
PROBLEMS

Questions of the Future. — Problem of Three Bodies. — Conception of
Approximation. — Object of Mechanics. — Simplicity of Description. — Limits
of Proof. — Reflections about the Circle. — From the History of Errors. —
Causalities. — Relativity on a Physiological Basis. — Physicists as Philosophers.

WE spoke of the objects and problems of science in
general, and touched on certain recurrent questions
with which reputed men of science are confronted
from time to time, so that we may ascertain their opinions about
immediate as well as more remote aims, and about worthy
objects and those within reach.

" Such stimuli," said Einstein, " may be quite Interesting
inasmuch as they sharpen the appetite of the pubHc for the
works of investigators, and give the latter the opportunity
of making wider circles acquainted with their plans. Yet
the value of their suggestions must not be overrated, when
they are directed at giving trustworthy information about the
future lines of development of science. Every scientist, in
working out his own research, gravitates to particular points
on the boundary which separates the known from the unknown,
and becomes inclined to take his particular perspective from
these points. It must not, however, be expected that these
individual aspects will form a complete picture, and will indicate
the only paths along which science can or will advance."

" May I suggest. Professor," I answered, " that we select
certain answers that have been given to these recurrent
questions for discussion ? I have brought along a whole series
of them ; it would be of value to know what attitude you take
up towards some of the statements that have been made about
future possibilities."

Einstein acquiesced, and so I read out a number of ex-
pressions of opinion, given by eminent authorities, particu-
larly in natural science and mathematics. They came under

143

144 EINSTEIN THE SEARCHER

the heading, " The Future Revolution of Science.'* At the
outset we encountered arguments by Bailhaud, the director
of the Paris Observatory ; he dealt with the so-called " Problem
of Three Bodies/* and with '* The Finitude or Infinitude of the
Universe."

Einstein elucidated these questions as follows. The cele-
brated Problem of Three Bodies is a special case of the general
problem of Many Bodies, the object of which is to discover the
exact paths of the heavenly bodies. If we suppose that the
planets and the comets are subject only to the attraction of
the central body, the sun, then their paths would be exactly
those given by Kepler's Laws — that is, they would move about
the central body, or, more precisely, about the common centre
of gravity in perfectly elliptical orbits. The same result would
happen if we regard the orbit of a moon to depend solely on
iti parent planet. But this assumption is not in agreement
with reality, since all the bodies of our system are also subject
to their mutual attraction depending on their masses and
distances. Consequently we have the so-called disturbances,
perturbations, and divergences from the ideal paths ; and the
problem of ascertaining these disturbances is essentially
identical with the Problem of Three Bodies. Regarded from
the point of view of pure mechanics, this problem may be
considered solved in so far as we are able to write down the
equations of motion. But, in addition to this purely
mechanical process, there is a mathematical problem which
has not been completely solved — ^that is to say, the integral
expressions that occur in it can be calculated only approxi-
mately. This makes no difference to the practical calculation,
since the degree of approximation, according to the present
methods, may be carried as far as we wish. The error may
be reduced to any desirable extent, so that it is probably wrong .
to expect new revelations on this point from future upheavals
in physics. We read on and discovered that several of the
scientists mentioned did not stop at expecting all advances
of the future from pure theory. They had visions of an
optimum of happiness, to gain which the increase of know-
ledge alone did not suffice. Thus the celebrated Swedish astro-
physicist Svante Arrhenius had summarized his judgment in
a few lines : " After the stupendous progress that has been

PROBLEMS 145

made in the physical and chemical sciences in recent times,
it seems to me that the moment has come for attacking the
most important problems of mankind with full success, namely,
those of biology, and in particular of the art of healing, with
the weapons that are furnished by the arsenal of the exact
sciences." And the mathematician, Emile Picard, Membra
de TAcademie, expressed himself in still more hopeful terms :
" There is no doubt but that the discoveries which the human
race is awaiting with impatience are those that are seeking to
eliminate sickness and the decrepitude of old age. Injections
giving immunity against all diseases, an elixir of life {une
eau de Jouvence) for persons of advancing age — these are the
discoveries that are longed for by every one. There are also
sciences that are to be termed ' moral,' from which we are
impatiently expecting that guidance which will diminish the
hate which seems to be increasing from day to day among
the nations. That would be a splendid discovery."

" These are, indeed, noble and inspiring words," said I.
" It shows how deeply rooted is the demand for ethical values
in human nature, when even a mathematician, whose intel-
lectual interests are directed primarily towards exact results,
ranks the discoveries of ethics above all others."

Einstein answered : *' We must carefully distinguish
between what we wish for in general and what we have to
investigate as belonging to the world of knowledge. The
question under consideration is not one of wishes and feelings,
but was unmistakably aimed at the advances and revolutions
in the realm of science. It does not come within the scope
of science at all to make moral discoveries 1 Its one aim is
rather the Truth. Ethics is a science about moral values,
but not a science to discover moral ' truths.' Ethics, conceived
as a science in the usual way, can therefore serve to discover
or to promote truth only indirectly. To illustrate my point
of view I shall quote an example taken from a totally different
field ; it is merely to serve as an analogy. Let us consider
the game of chess. Its value and its meaning is not to be
sought in scientific factors, but in something entirely different,
in a struggle which takes place according to definite rules.
But even chess, inasmuch as it sharpens the intellect, may
exhibit an indirect value for promoting truth. It may, for

lO

146 EINSTEIN THE SEARCHER

instance, suggest examples in permutations, which may con-
tain mathematical, that is, purely scientific, truths. I certainly
do not deny that there is an ethical factor in all genuine
sciences. For being occupied with things for the sake of
truth alone emancipates and ennobles the mind."

" This ennobling effect," I interposed, " should surely show
itself in a moderation of the passions which were mentioned
in the above expression of opinion. With Picard we should
expect above all things to see a diminution in the feelings of
hate between peoples, the tragic consequences of which we
have experienced."

Einstein smiled, and, with a touch of sarcasm, said, *' Hate
is presumably a privilege of the ' cultured,' who have the time
and the energy for it, and who are not the slaves of care." His
tone indicated clearly that he used the generic term " cultured "
to denote the Philistines of culture, its snobbish satelUtes, but
not those whose intensive work aimed at increasing and
deepening the fields of culture. In general he maintained his
view that it is an illusion to expect " discoveries " in the
realm of ethics, since every real discovery belonged alone to
the sphere of truth in which the division only into right and
wrong, not that into good and evil, holds good.

This led us to the old question of Pilate : What is Truth ?
In seeking an answer to this question Einstein first called
special attention to the conception of " approximation,"
which plays a great part in the actual search for truth, inas-
much as every physical truth, expressed in measures and
numbers, always leaves some remainder, that marks its
distance from the unattainable truth of reality. This con-
ception, which manifests itself so prominently in the relation
of Einstein's own researches to the older, so-called classical,
mechanics, will be developed here according to his line
of thought as far as I can recollect from a number of
conversations.

Let us suppose that we overhear two people arguing about
the shape of the earth's surface. The one afi&rms that it is an
unHmited plane, whilst the other maintains that it is a sphere.
We should not hesitate a moment to say that the first is in error,
and that the second gives the true answer. As long as the
question was to be decided in favour of a " Plane or a Sphere,"

PROBLEMS 147

the sphere would represent the absolute truth. Yet it would
be only relative, for these two statements are contradictory
only between themselves, but will no longer be so if a third
assertion is made which opposes a new alternative to
" sphere/'

If this alternative objection is actually raised, the third
person would be quite justified in saying that the " sphere "
explanation is wrong. For the conception " sphere *' re-
quires that all diameters be equal, whereas we know that they
are not so, since the distance from pole to pole has been proved
to be smaller than that between opposite points on the equator.
The earth is an ellipsoid of rotation, and this truth is absolute
in the face of the errors which are expressed by the terms,
plane and sphere.

It would again have to be added that this absoluteness
would stand only as long as this contradiction is regarded as
being one between a definite sphere and a definite ellipsoid.
If, as in the case of the earth, there are quite different diameters
in the equatorial and the diametral planes, then there is
complete contradiction between the two statements, and as
the supporter of the ellipsoid is right, the one who supported
the sphere must now give in, although he previously
triumphed over his first opponent. His statement was true
compared with the latter, but showed itself to be an error
when compared with the statement of the third person.

This does not run counter to the laws of elementary logic.
One of these, somewhat inadequately called the Law of Con-
tradiction, states that two directly contrary statements — e.g.
this figure is a circle, and this figure is not a circle — cannot
both be true simultaneously. The truth of the one implies
necessarily the falseness of the other. As this cannot be dis-
puted, it follows in our case that we cannot have been con-
fronted with contradictory judgments at all concerning the
figure of the earth.

This is to be understood in a geometrical sense. The
sphere does not entirely contradict the ellipsoid, since it is a
limiting case of the latter : and the plane is Hkewise a limiting
case of the sphere, as well as of the surface of ellipsoids.

But we are not concerned with purely geometrical con-
siderations, for the earth is a definite body, and not a limiting

148 EINSTEIN THE SEARCHER

configuration derived from abstraction. We are here dealing
with measurable quantities, whose difference can be proved,
and hence we must have one of the disputants proclaiming the
absolute truth, whilst the other proclaims an absolute error.
This, however, again is incompatible with our result that
the second person is right in the one case and wrong in the
other.

The logical Law of Contradiction overcomes the dilemma
in the simplest way. None of these assertions contains the
truth, hence none of these judgments allows the falseness of
the others to be deduced. Only this may be said, that there
is a fraction of truth in each judgment. The true shape of the
earth is given by the plane to a first, the sphere to a second,
the ellipsoid of rotation to a third, degree of approximation :
we reserve the right of further approximations, each of which
in succession approaches a higher degree of correctness, but
none attains the absolute truth.

This reflection on a particular case may be generalized, and
remains when we extend it to our attempts at grasping the
states, changes, and occurrences of Nature. Whenever we
talk of physical laws, we must bear in mind that we are deahng
with human processes of thought, that are subjected to a
succession of judgments, courts of appeal, as it were, excluding,
however, a final court beyond which no appeal is possible.
Each new experience in the course of natural phenomena may
render necessary a new trial before a higher court, whose duty
is then to give a more definite or different form to the law
formulated by us, so as to attain a still higher degree of
approximation to the truth.

If we call to mind some of the most valuable statements
made by modern investigators about the nature of natural
laws, we recognize that they are all connected by a single
thread of thought, namely, that even in the most certain law
there is left a remainder that has not been accounted for, and
that obliges us to consider a greater approximation to the truth
as possible, even if a final stage is not attainable.

Mechanics furnishes us with the expression of its laws in
equations, whose importance Robert Kirchhoff explained in
1874 by a definition that has been considered conclusive by
scientists. According to him, it is the object of mechanics to

PROBLEMS 149

describe completely (and not to explain) in the simplest manner
the motions that occur in Nature.

The postulate of simplicity is derived from the fundamental
view of science as an economy of thought. It expresses the
will of man's mind to arrive at a maximum of result by using
a minimum of effort, and to express the greatest sum of experi-
ence by using the smallest number of symbols. Let us con-
sider two simple examples quoted by Mach. No human brain
is capable of grasping all the possible circumstances of bodies
falling freely, and it may well be doubted whether even a
supernatural mind like that imagined by Laplace could succeed
in doing so. But if we take note of Galilei's Law for Falhng
Bodies and the value of the acceleration due to gravity, which
is quite an easy matter, we are equipped for all cases, and have
a compendious formula, accessible to any ordinary mind, that
allows us to picture to ourselves all possible motions of falling
bodies. In the same way no memory in the world could retain
all the different cases of the refraction of light. Instead of
trying to do the impossible task of grasping this infinite abund-
ance, we simply take note of the sine law, and the indices of
refraction of the two media in question ; this enables us to
picture any possible case of refraction, or to complete it, since
we are free to relieve our memories entirely by having the
constants in a book. Thus we have here natural laws that
give us a comprehensive yet abbreviated statement of facts,
and satisfy the postulate of simplicity to a high degree.

But these facts are built up on experiences, and it is not
impossible that some new unexpected experience will reveal
a new fact, which is not sufficiently taken into account in the
law. This would compel us to correct the expression for the
law, and to seek a closer approximation for the enlarged
number of facts.

The Law of Inertia, according to our human standard,
seems unsurpassable in simplicity and completeness ; it seems
to us fundamental. But this law, which prescribes uniform
rectilinear motion to a body subject to no external forces,
selects only one possibiHty out of an infinite number as being
valid for us. It does not seem evident to a child, and it is
easy to imagine a good scholar in some branch of knowledge
other than physics, to whom it would hkewise not seem evident.

150 EINSTEIN THE SEARCHER

For it is by no means necessary a priori that a body will move
at all when all forces are absent. If the law were self-evident,
it would not need to have been discovered by Galilei in 1638.
Nevertheless, it appears to us, now, to be absolutely self-evident,
and we can scarcely imagine that it can ever be otherwise.
This is simply because we are bound to the current set of ideas
that cannot extend beyond the sum of sense-data and experi-
ences that have been inculcated into us by heredity and en-
vironment. At a very distant date in the future the average
mind may surpass that of Galilei to the same extent as Gahlei's
surpasses that of a child, or of a Papuan native. And of all
the infinite possibilities one may occur to a Galilei of the distant
future, which, when formulated as a law, may serve to describe
motions of a body subject to no forces better than the law of
inertia, proposed in 1638.

These reflections are not mere hallucinations, but have to
do with scientific occurrences that we have observed in the
twentieth century. Newton's equation that gives the Law of
Attraction is beyond doubt a model of simplicity, and it would
have occurred to no thinking person of even the last generation

to doubt its accuracy. The easily grasped expression k — ^

apparently expresses truth in a law which is valid for all
eternity. In this expression, he denotes a gravitational con-
stant, that is, a quantity which is invariable in the whole uni-
verse ; m and rn^ are two masses that act attractively on one
another ; and r is the distance between them. But Newton
has been followed by Einstein, who has proved that this ex-
pression represents only an approximate value, that leaves a
small remainder as an error that may be detected if the greatest
refinement be made in our methods of observation. The
equations that have been set up by Einstein represent the
approximation that is to be considered final for the present,
and that may remain valid for thousands of years. They are
certainly very complicated, being included in a system of
differential equations of awe-inspiring length, and we may
feel tempted to object with the question : how do they agree
with Kirchhoff' s postulate that the simplest description of the
motions must be sought ? But this objection falls to the
ground if we look carefully into the question. For simpHcity

PROBLEMS 161

consists not merely in being brief or in excluding difficulty
from a formula, but rather in asserting the simplest relation
to the universe as a whole, which is independent of all systems
of reference. When this independence is proved — and in
Einstein's case it is so — the complicated aspect of the formula
disappears entirely in the light of the higher simplicity and
unity of the world-system that presents itself — a world-system
that is directed in conformity with the one fundamental law of
general relativity as well in the motion of the electrons as in
motion of the most distant stars. With regard to the other
postulate, that of completeness, i.e. absolute accuracy, we
have been furnished with proofs that have rightly excited the
wonder of the present generation. But are we then to recognize
the Principle of Approximation in every direction ? Is there
then nothing that can be proved rigorously, nothing that is
unconditionally valid in the form of knowledge that corresponds
exactly to truth ?

We are led to think of mathematical theorems, which,
when they have once been proved, are evident to the same
degree as the axioms from which they have been derived, by
virtue of logic which cannot be disputed since a contradiction
leads to absurdity. It has been said that mathematics est
scientia eorum, qui per se clara sunt, that is, is the science of
what is self-evident.

But here again doubts arise. If we should get to know
only a single case, in which the self-evident came to grief, the
road to further doubts becomes open. Such a case will now
be quoted.

As we know, a tangent is a straight line, which makes
contact with a curve at two coincident (or infinitely near)
points without actually cutting the curve. The simplest case
of this is the perpendicular at the extremity of a radius of a
circle. And it agrees fully with what our feeling leads us to
expect when it is stated that every curved line that is " con-
tinuous," that is, which discloses no break and no sudden bend,
has a tangent at every point. Analysis, which treats plane
curves as equations in two variables, gives the direction of the
tangent in terms of the differential coefficient, and declares
accordingly that every continuous function has a differential
coefficient, that is, may be differentiated, at every point. The

152 EINSTEIN THE SEARCHER

one statement amounts to the same as the other, since there
must be an equivalent graphical picture corresponding to every
functional expression.

But this apparently rudimentary theorem involves an
error, which was not discovered before the year 1875. The
theory of curves has been in existence for centuries, but it
occurred to no one to doubt the general validity of this theorem
of tangents. It was regarded as self-evident, as a mathe-
matical intuition. And certainly neither Newton, nor Leibniz,
nor Bernoulli, not to mention the mathematicians of olden
times, even dreamed that a continuous curve without a tangent,
or a continuous function without a differential coefficient,
was possible.

Moreover, a proof of the theorem had been accepted. It
appeared in text -books, and was often to be heard in lecture
rooms ; nor was a shadow of a doubt suggested. For it was
not merely a demonstratio ad oculos, but it appeared directly
to our sense of intuition. And we may safely say that up to
the present day no one has ever been able to imagine a con-
tinuously curved Hne which has no tangent ; no one has been
able to picture even one point of such a curve at which no
tangent could be drawn.

Nevertheless, scientists appeared who began to entertain
doubts. In the case of Riemann and Schwarz these doubts
assumed a concrete form, in that they proved that certain
functions are refractory at certain points. But Weierstrass
was the first to make a real breach in the old belief that was so
firmly rooted. He set up a function that is continuous at every
point, but differentiable at no point. The graphical picture
would thus have to be a continuous curve having no tangent
at all.

What is the appearance of such a configuration ? We do
not know, nor shall we presumably ever get to know. During
a conversation in which this problem of Weierstrass arose,
Einstein said that such a curve lay beyond the power of
imagination. It must be remarked that, although the mathe-
matical expression of the Weierstrass function is not exactly
simple, it is not inordinately complex. Moreover, seeing that
one such function (or curve) exists, others will soon be added
to it (Poincare mentions that Darboux actually gave other

PROBLEMS 153

examples even in the same year that the first was discovered) ;
there will, indeed, be found an infinite number of them. We
may go still further, and say that, corresponding to each curve
that has tangents, there are an infinite number that have
no tangents, so that the former form the exception and not the
rule. This is an overwhelming confession that shakes the
foundations of our mathematical convictions, yet there is no
escape.

How may we apply the principle of '* approximation " to
these considerations ? May we say that the theorem that was
beheved earlier is an approximation to a mathematical truth ?

This is possible only conditionally, in a certain extremely
limited sense, namely, if we picture to ourselves that point
in the development of science at which the conception and
properties of tangents first began to be investigated. Com-
pared with this stage of science, the above theorem denotes a
first approximation to the truth, in spite of its incorrectness ;
for it makes us acquainted with a great abundance of curves
that are very important for us and that exhibit tangents at
every point. This knowledge brings us a step nearer to the
more approximate truth given by Weierstrass's example.
In the distant future, the earnest student will learn this theorem
only as a curious anecdote, just as we hear of certain astro-
logical and alchemistic fallacies. He will learn, in addition,
other theorems that are looked on as proved by us of the present
day, although actually they were proved only approximately.
For what does it mean when Gauss, for example, repudiated
certain proofs of earlier algebraists as being " not sufficiently
rigorous," and replaced them by more rigorous proofs ? It
signifies no more than that, in mathematics, too, what appears
to one investigator as flawless, strict, and evident, is found by
another to have gaps and weaknesses. Absolute correctness
belongs only to identities, tautologies, that are absolutely true
in themselves, but cannot bear fruit. Thus at the foundation
of every theorem and of every proof there is an incommensurable
element of dogma, and in all of them taken together there
is the dogma of infallibihty that can never be proved nor
disproved.

It must appear extremely interesting that, at first sight,
this example of the tangent has its equivalent in Nature

154 EINSTEIN THE SEARCHER

herself, namely, in molecular motions the investigation of
which is again largely due to Einstein.

Jean Perrin, the author of the famous book, Atoms, describes,
in the introduction, the connexion between this mysterious
mathematical fact and results that are visible and may be
shown by experiment, to which we have been led by the study
of certain milky-looking (colloidal) liquids.

If, for example, we look at one of those white flakes, which
we get by mixing soap solution with common salt, we at first
see its surface sharply outlined, but the nearer we approach
to it, the more indistinct the outline becomes. The eye
gradually finds it impossible to draw a tangent to a point of
the surface ; a straight line which, viewed superficially, seems
to run tangentially, is found on closer examination to be
oblique or even perpendicular to the surface. No microscope
succeeds in dispelhng this uncertainty. On the contrary,
whenever the magnification is increased, new unevennesses
seem to appear, and we never succeed in arriving at a continuous
picture. Such a flake furnishes us with a model for the general
conception of a function which has no differential coefficient.
When, with the help of the microscope, we observe the so-
called Brownian movement, which is molecular by nature,
we have a parallel to the curve which has no tangent, and
the observer is left only with the idea of a function devoid
of a differential coefficient. . . . We find ourselves obHged,
ultimately, to give up the hope of discovering homogeneity
at all in stud5dng matter. The farther we penetrate into its
secrets, the more we see that it, matter, is spongy by nature
and infinitely complex ; all indications tend to show that closer
examination will reveal only more discontinuities.

I have not yet had an opportunity of seeing these Brownian
movements under the microscope, but I must mention that
Einstein has repeatedly spoken to me of them with great
enthusiasm, of an objective kind, as it were, for he betrayed
neither by word nor by look that he himself has done research
leading to definite laws that have a recognized place in the
history of molecular theory.

As soon as we approach the question of molecular ir-
regularities we recognize that, when we earlier spoke of the
figure of the earth in discussing the principle of " approxima-

PROBLEMS 155

tion," we were still very far from the limit that may be
imagined. We had set up the three stages : plane — sphere —
elUpsoid of revolution, as relative geometrical steps, beyond
which there must be still further geometrical approximations.
If we imagine all differences of level due to mountains and
valleys to be eliminated, for example, and if we suppose the
earth's surface to consist entirely of liquid, undisturbed by the
sHghtest breath of wind, even then, the elHpsoid is by no means
the final description. For now the discontinuities from mole-
cule to molecule begin, the infinite number of configurations
without tangents, the macroscopic parallels of what the white
flake soap solution showed as microscopically, and no conceiv-
able geometry would ever be adequate to grasp these pheno-
mena. We arrive at a never-to-be-completed list of functions
which can never be described either in words or in symbolic
expressions of analysis.

But even if the ultimate geometrical truth is hidden behind
the veils of Maya,* we are yet left with the consolation that the
method of approximation, even when applied to a relatively
modest degree, produces remarkable results in the realm of
numbers. Let us consider for a moment in the simple figure
of a circle the ratio between the circumference and the radius.

As we know, this ratio is constant, and is called in honour
of the man who first gave a trustworthy value for it, Ludolf's
number, namely, tt (pi). Thus it makes no difference whether
we consider a circle as small as a wedding-ring, or as large as
a circus arena, or even one the radius of which is as great as
the distance of Sirius. And it makes just as little difference
what happens to the circle whilst it is being measured ; the
above ratio must remain constant.

But here, too, a contradiction makes itself heard, issuing
from one section of modern science. It calls to mind the
saying of Dove that when professors are not quite sure about
a thing they always preface their remarks with the phrase :
"it is well known that*' . . . We should be well advised in
avoiding this method of expression altogether, for even when
we feel quite sure, the ghost of the unknown lurks behind
what we fain would call well known.

The theorem that all circles without exception are subject

♦ Maya = appearance.

156 EINSTEIN THE SEARCHER

to the same measure-relation belongs a priori to the S3mthetic
judgments. But fields of thought have been discovered in
which the a priori has lost its power. Mathematics — once
a quintessence of synthetic statements a priori — is now
regarded as being dependent on physical conditions. Physical
conditions, however, are empirical and subject to change.
Therefore, since the a priori is not subject to change, we
encounter a discrepancy. It leads to the question : Is the
Euclidean geometry with which we are famiHar the only
possible geometry ? Or, in particular : Is tt the only possible
measure-relation ?

Einstein rephes in the negative. He not only shows how
another geometry is possible, but he also discloses what once
seemed inconceivable, namely, that if we wish to describe
the course of the phenomena of Nature exactly by means of
the simplest laws, it is not only impossible to do so with the
help of Euchdean geometry alone, but that we have to use a
different geometry at every point of the world, dependent
on the physical condition at that point.

From the comparatively simple example of two systems
rotating relatively to one another, Einstein shows that the
peripheral measurement of a rotating circle, as viewed from
the other system, exhibits a peculiarity which does not
accompany the radial measurement. For, according to the
theory of relativity, the length of a measuring rod is to be
regarded as being dependent on its orientation. In the case
quoted, the rod undergoes a relative contraction only when
applied along the circumference, so that we count more steps
than when we measure the circumference of the same circle
at rest, that is, in non-rotation. Since the radius remains
constant in each case, we %<^\, a relatively greater value for tt,
which shows that we are no longer using Euclidean geometry.

Yet, formerly, before such considerations could even
be conceived in dreams, this tt was regarded as absolutely
established and immutable ; and observers used every possible
means of determining its value as accurately as possible.

In Byzantium there Hved during the eleventh and twelfth
centuries a learned scholar, Michael Psellus, whose fame as
the " Foremost of Philosophers " stretched far and wide,
and whose mathematical researches were regarded as worthy

PROBLEMS 157

of great admiration. This grand master had discovered by
analytical and synthetical means that a circle is to be regarded
as the geometric mean between the circumscribed and the
inscribed square, which gives to the above quantity, as may
easily be calculated, the value \^S, that is, 2*8284271. . . .
In other words, the length of the circumference is not even
three times that of the radius.

We have the choice of regarding the result of Psellus as
an approximation, or as mere nonsense. Every schoolboy
who, in a spirit of fun, measures a circular object, say a top,
with a piece of string, arrives at a better result, but the con-
temporaries of Psellus accepted this entirely wrong figure
with credulous reverence, and continued to bum incense at
the feet of the famous master. It is all very well for us of
the present to call him a donkey. We have just as much
right in saying that mathematicians differ, not in their natures,
but only in the order of their brain functions. If a man like
Psellus missed the mark by so much, it is possible that men
like Fermat or Lagrange may also have erred occasionally
or even consistently.

No heavenly power will give us a definite assurance to
the contrary, and all of us may be just as false in our judgment
of accepted celebrities as were the Byzantines eight hundred
years ago in their estimate of Psellus.

Whereas the latter had obtained a value " less than 3,"
there are learned documents of about the same date that have
been preserved, according to which the value of ir comes out
as exactly 4. Compared with this grandiose bungling, even
the observations mentioned in the Old Testament are models
of refinement. For, as early as three thousand years ago,
it is stated of the mighty basin in the temple of Solomon
(First Book of Kings, chapter vii.) : " And he made a molten
sea, ten cubits from the one brim to the other : it was round
all about, and his height was five cubits ; and a line of thirty
cubits did compass it round about." Thus tt here appears
as 3, an approximation which no longer satisfied later genera-
tions. The wise men of the Talmud went a step further,
in saying 3 plus a little more ; and this agrees roughly with
the actual value.

The view became more and more deeply rooted that this

158 EINSTEIN THE SEARCHER

TT was |a main pillar of mathematical thought and calculation.
The more the problem of the quadrature of the circle seized
on men's minds, the greater were the efforts made to find
the exact value of this " little more " of the Talmud. Since
1770 we know that this is not possible, for tt is not rational,
that is, it can be represented only as an infinite and irregular
(that is, non-repeating) decimal expression. It occupies,
further, a special rank as a transcendental quantity ; this
fact was proved by Lindemann as late as 1882 for the first
time. Yet, even nowadays, there are incorrigible devotees
of quadrature, who are still hunting a solution because they
cannot rid themselves of the hallucination that such a simple
figure as the circle must submit ultimately to a constructive
process.

The correct way was to carry out an even more accurate
determination of the decimal figures. The above-mentioned
Ludolf van Ceulen got as far as the 35th place of decimals ;
at the turn of the eighteenth century the looth decimal
place was reached. Since 1844, thanks to the lightning
calculator Dase, we have its value to the 200th decimal place,
and this should satisfy even the most extravagant demands.
This number, associated with the circle, is a classical example
of how an approximation that is expressible in figures of very
small value gives an order of accuracy that can be described
only by using fantastic illustrations.

If we take a circle of the size of the equator, and also
multiply the value of the diameter of the earth by tt, we know
that the latter result will not be exactly equal to the former,
and that there will always be a small remainder. If this
discrepancy were less than a metre, the order of exactness
would be extraordinarily high, for a metre is practically
insignificant compared with a mighty circle of the dimensions
of the earth's circumference.

Let us stipulate still greater accuracy. We demand that
the error is to be less than the thickness of the thinnest human
hair. We find, then, that we must take for tt at most 15
places of decimals. Thus, if we use 7'" = 3*14159265358973,
we are applying a means of calculation that reduces the
possible error in all measurements of circles on the earth
to a degree beyond the limits of human perception.

PROBLEMS 159

If we pass beyond the world out into celestial space, and
consider circles of the dimensions of a planetary orbit, nay,
further, if we pass on to the Milky Way or even to the limit of
visible stars, to find space for our circle, and if in this case we
still reduce the discrepancy so as to be less than any length
that is observable under a microscope, then the last given
value of TT still suffices. Yet we must not forget the proviso :
semper aliquid haeret, something unsolved still cHngs to the
problem.

Such numerical approximations, however instructive they
may be, nevertheless retain a comparatively playful character,
and furnish only a superficial analogy to the most important
approximations that are contained in our natural laws them-
selves. It is these, above all, that manifest themselves so
clearly in Einstein's Hfe-work, and they bear the same relation
to the former as truth bears to correctness. Truth comprises
the greatest conceivable circle of ideas and passes far beyond
the sphere of correctness, which deals only with measure-
relations, and not with the things in themselves. If Einstein,
as we learn, emphatically declares truth to be the only object
of science, he means the strictly objective truth that is to be
derived from Nature, the true relationship of phenomena and
occurrences, independently of whether restless philosophy
assigns a question mark to this ultimate objectivity. A great
discoverer in the realm of Nature cannot and dare not proceed
otherwise. For him there is behind the veil of Maya not a
phantom that finally vanishes, but something knowable, that
becomes ever clearer and more real as he detaches each suc-
cessive veil in his process of approximation.

During this conversation, when we were talking of the
" Future of the Sciences," Einstein gave his ideas free rein,
shooting far ahead of the views and prognostications of the
above-mentioned scientists :

" Hitherto we have regarded physical laws only from the
point of view of Causality, inasmuch as we always start from
a condition known at a definite cross-section of time, that is,
by taking a time-section of phenomena in the universe, as, for
example, a section corresponding to the present moment. But,
I believe," he added, with earnest emphasis, " that the laws of
Nature, the processes of Nature, exhibit a much higher degree

160 EINSTEIN THE SEARCHER

of uniformity of connexion than is contained in our time-
causality I This possibiHty suggests itself to me particularly
as the result of certain reflections concerning Planck's Quantum
Theory. The following may be conceived : What belongs to
a definite cross-section of time may in itself be entirely devoid
of structure, that is, it might contain everything that is physi-
cally conceivable, even such things (so I understood him to say)
as, in our ordinary physical thought, we consider impossible
of realization, for example, electrons of arbitrary size, and
having an arbitrary charge, iron of any specific gravity, etc.
By our causality we have adjusted our thought to a lower
order of structural limitations than seems realized in Nature.
Real Nature is much more limited than our laws imply. To
use an allegory, if we regard Nature as a poem, we are like
children who discover the rhyme but not the prosody and the
rhythm." I interpret this as meaning that children do not
suspect the restrictions to which the form of the poem is
subject, and just as httle do we, with our causahty, divine
the restrictions which Nature imposes on occurrences and
conditions even when we regard them as governed by the
natural laws we have found.

Thus a leading problem of science in the future will be
to discover the restrictions of Nature as compared with the
apparent causality implied in physical laws.

We have in this an example of the transcendental per-
spectives that are opened up when we accompany Einstein
on one of his excursions of thought. In this case it is actually
a question of ultimate things, of a region of discovery of
which we cannot yet form a conception, and it appears
doubtful whether the problems latent in it are to be treated by
making investigations into physical nature, or whether they
^re to be allotted to speculative philosophy.

In the first place, Einstein's remark seems to aim at nothing
less than a revision of the conception of causality. However
much has been done to purify this conception and to make it
clear, we have here, perhaps, a new possibility of refining it
by making a synthesis of scientific and abstract philosophical
views. We shall just touch very Hghtly and superficially on
the possibility of a synthesis giving us an avenue to truth.
Whoever has heard these words of Einstein, feels the need of

PROBLEMS 161

getting on to firm ground to rescue himself out of the turmoil
of ideas into which he has been plunged.

What is Causahty ? A physiological answer may be given
by saying that it is the irrepressible animal instinct, rooted
in our brain-cells, that compels us to connect together things
that we have experienced and imagined. Poets have defined
Hunger and Love as the fundamental elements of our social
lives ; we need only add the thirst for causahty to this to
complete the Hst of primary instincts. For this mental thirst
is not less intense than our bodily hunger, and is even greater
in that it never forsakes us for a moment. It is easier for the
body to check breathing than for the soul to still the question
of the why and wherefore, of the cause and effect, of the ante-
cedent and consequent.

This ceaseless search for a connexion between occurrences
has become organized into a fixed and immovable form of
thought, which remains mysterious even when we imagine
that we have eliminated all the mystery from it. The rela-
tions that we seek and that we regard as being of an elementary
character are totally foreign to Nature herself. David Hume,
the first real, and at the same time the most penetrating,
explorer into this form of thought, said that, in the whole of
Nature not a single case of connexion is disclosed which we
are able to grasp. All happenings appear, in reahty, dis-
connected and separate. One " follows on " another, but we
can never detect a connexion between them. They appear
" co-joined," but never " connected." And since we can form
no idea of what has never presented itself to our outer or inner
perception, the necessary conclusion seems to be that we have
absolutely no idea of causal connexions or causative forces,
and that these expressions are quite devoid of meaning, how-
ever much they may be used in philosophical discussions or
in ordinary life. This " Inquiry concerning Human Under-
standing," with its atmosphere of resignation, has been ela-
borated in manifold ways, particularly by Kant and the
Kantians ; for it is impossible to take up a philosophic thread
without entering on an examination of the fundamental
question concerning the existence of a causality which lies
outside our instinct for causahty. It is also inevitable that,
whenever we start '^ut in this direction, we encounter the
II

162 EINSTEIN THE SEARCHER

further question : What is Time ? For causality directs
itself to the problem of succession, both of sensations and
phenomena, consequently the two questions are not only
intimately connected, but are really only different expressions
of one and the same question. Time, which according to
Descartes and Spinoza is a modus cogitandi, not an affectio
rerum, and, according to Kant, is an a priori form of thought,
dominates our intelHgence with the same sovereign power, as
the imagined course of things : what we perceive in the corre-
sponding act of thought is regarded as temporal and causal,
and impossible of further analysis.

Now, the conception of time has been entirely revolu-
tionized by Einstein himself ; and it may be expected that
the conception of causahty, too — which, in accordance with
custom, we still endow with a separate existence — will also be
affected by this revolution.

We thus approach a relativization of causaUty, and we
may advance a step further in this direction, if we call to mind
the differences of time-perception that Nature herself leaves
open to us. It must be clearly understood that we are not
dealing at present with the theoretical time of physics, in
the sense of Einstein's theory, but with something physio-
logical that ultimately, however, resolves itself into a rela-
tivization of time, and hence also of the causal connexions in
time.

To do this, we have to follow the lines of reasoning de-
veloped by the celebrated St. Petersburg academician, K. E.
von Baer, and we need extend it only very httle to get at
the heart of causality, if we start from his address of i860 :
" Which View of Living Nature is correct ? " For the human
brain is a part of Hving nature, and hence the processes of
thought may also be conceived as expressions of hfe.

The starting-point is a figment, the fictitious character
of which vanishes as soon as we approach its results. The
bridge of thought may be destroyed later ; it suffices to carry
us temporarily, as long as it lands us in safety on the other
side.

The rapidity of perception, of the arbitrary motions, of
intellectual life seems in the case of various animals to be
proportional approximately to the rapidity of their pulse-

PROBLEMS 168

beats. Since, for example, the pulse of a rabbit beats four
times as quickly as that of a bull, it will, in the same interval
of time, also perceive four times as quickly, and will be able
to execute four times as many acts of will, and will experience
four times as much as the bull. In the same astronomical
length of time the inner life and perceptual world, in the case
of various animals, including Man, will take place at different
specific rates, and it is on these rates that each of these living
creatures bases its subjective measure of time. Only when
compared with our own measure of time does an organic
individual, say, a plant, appear as something permanent in
size and shape, at least v^ithin a short interval. For we may
look at it a hundred times and more in a minute, and yet
notice no external change in it. Now, if we suppose the
pulse-beat, the rate of perception, the external course of life,
and the mental process of Man, very considerably accelerated
or retarded, the state of affairs becomes greatly changed,
and phenomena then occur, which we, fettered by our
physiological structure, should have to reject as being fantastic
and supernatural, although, on the supposition of a new
structure they would be quite logical and necessary. If we
suppose human life from childhood to old age to be compressed
into a thousandth part of its present duration, say, into a
month, so that the pulse beats a thousand times more quickly
than occurs in our own experience, we should be able to follow
the course of a discharged bullet very exactly from point to
point with our eyes, more easily than we can at present observe
the flight of a butterfly. For now the motion of the bullet
in a second will be distributed among at least looo pulse-
beats, and will induce at least looo perceptions, and accord-
ingly, in comparison with our everyday perception, it will
appear looo times slower. If the duration of our hfe were
again to be reduced to a thousandth of its first reduced value,
that is, shortened to about forty minutes, then our flowers
and herbs would seem just as motionless and immutable as
rocks and mountains, in which we only infer the changes
without having directly observed them. We would in the
course of our lives see little more of the growth and decay of
a bud and a flower in full bloom than we at present see of
the geological changes in the earth's crust. The acts of

164 EINSTEIN THE SEARCHER

animals would be much too slow to be seen ; at most, we
could infer them as we do the motions of the stars at present.
If life were shortened still further in the same way, light
would cease to be an optical occurrence to us. Instead of
seeing the things on which light falls, we should become
aware of them as being audible, and what we at present call
tones and noises would long have ceased to have an effect
on the ear.

If, however, we let our fancy roam in the opposite direction,
that is, if, instead of compressing the duration of human
life, we expand it enormously, what a different picture of
the world would present itself ! If, for example, the pulse-
beat, and hence the rate of perception, were to be made a
thousand times slower, so that the average human life would
be spread o^t over, say, 80,000 years, and that we should
experience in one whole year only as much as we now ex-
perience in a third of a day, then, in every four hours winter
or any other season would pass by, vegetation would spring
up and as rapidly die. Many a growth would not be per-
ceptible, on account of its relative rapidity compared with
the rate of the pulse-beat. For example, a mushroom would
suddenly come into existence, Hke a newly formed spring.
Day and night would alternate as a Hght and a dark minute ;
and the sun would appear to fly over the heavens like a fiery
projectile. If we were again to make the duration of human
life a thousand times longer still, and hence the rate of hfe
a thousand times slower still, we should, during the whole of
an ordinary year, be able to have only 190 distinct perceptions,
so that the difference between day and night would vanish
entirely, and the sun's path would be a glowing circular
band in the heavens, and all changes of form that seem to us
to happen quietly and regularly, and to preserve a certain
permanency, would melt together in the wild stream of
happening, engulfed in its onward rush.

Are we justified in opposing to this relative perception
of time " our own *' time, which is something specific and
dependent on our constitution as human beings ? Should
we not rather adopt the view that this specific time, adapted
to our particular pulse-beat, gives only a very limited picture
of the world, which is conditioned and determined by the

PROBLEMS 165

limitations of our own definite intelligence ? Is it, perhaps,
only a distorted picture, a caricature, of actual occurrences ?

An intelligence infinitely superior to our owti would no
longer be dependent on the separate sensations such as are
presented to us with the rhythm of the pulse. For such a
mind there would be no metronomic foundation in the sequence
of occurrences, beyond what represents itself as time to our
understanding. He would be situated outside of time in what
Thomas Aquinas called the nunc sians, in the stationary
present, without a retrospect of the past and without ex-
pectation of a future. Without the Before and the After, the
occurrences of the world would acquire the clearest and
simplest meaning, hke that given by an equation of identity.
What presents itself to us as a " succession " of events would
merge together into one whole, just as a succession of numerical
calculations become summarized in a rule of calculation, or
as a series of logical operations resolves into a logical self-
evident truth. If the mind conceived by Laplace actually
existed, it would stand above the necessity of introducing
time as a quantity into its world-equations, for time is a
purely anthropomorphic quantity, produced by our percep-
tion, and regulated by our own characteristic pulses. Accord-
ingly, the conception of causaUty, too, which is indissolubly
connected with time, must be regarded as anthropomorphic,
as something that we read into, and not out of. Nature. We
should at least have to recognize that if there is a causality
outside ourselves, then we can learn only a minimum about
it, and even this only in a w^orld displaced or distorted by
the accidental rate of oiu: pulse-beat.

Let us now repeat Einstein's assertion *' that the laws of
Nature, the processes of Nature, exhibit a much higher degree
of uniformity of connexion than is contained in our time-
causaUty ! It is possible that what belongs to a definite
cross-section of time may in itself be entirely devoid of struc-
ture, that is, it might contain everything that is physically
conceivable, even such things as, in our ordinary physical
thought, we consider impossible of realization, for example,
iron of any arbitrary specific gravity." It seems to me that
the non-physicist will, perhaps, gain a clearer insight into these
highly significant words of Einstein, now that he has received

166 EINSTEIN THE SEARCHER

the assistance of these physiological considerations. It must
be granted that the philosophic grounds of Einstein are quite
different and lie much deeper than those of von Baer, who
starts from organic functions and ends by arriving at a
mysterious relativity that is yet consistent in itself. Never-
theless, there is one point of contact, inasmuch as in each case
possibiUties that lie apparently extra naturam are suggested.

Einstein says : ' * Hitherto we have regarded physical laws
only from the point of view of causality, inasmuch as we always
start from a condition known at a definite cross-section of
time, as, for example, a section corresponding to the present
moment." At our own risk an easy paraphrase of his words
will be attempted :

The time-section of the present contains for us the sum
of all previous experiences, out of which the necessary course
of our thought sifts out the category of causality.

What is not present in experience cannot appear in our
causality. Let us consider for a moment Hume's example of
the Indian who has never known ice. Without being told,
and if he is dependent only on his own sensations, he would
never learn that water freezes in cold cUmates. The influence
of cold on water is not gradual, corresponding to an increase
of cold, and not one that may be anticipated in all its conse-
quences, but at the freezing-point water, which a moment
before was a very mobile liquid, passes into a very rigid solid.
The causahty of the Indian cannot account for this. If we
tell him of this phenomenon, he has two courses open to him.
Either he refuses to believe it — and this would be quite
natural, since rigid water is to him as meaningless as is a square
circle to us. Or else he believes the story, and then his list
of categories incurs a break, passing through the middle of
causahty. He has then to reconcile himself to the assumption
that something that is meaningless to him and that stands out-
side the connexion of cause and effect is possible of realization.
Up to that moment, in his time-section of the present, there
was no room for it in his causality. To Torricelli the concep-
tion of Hquid air, which we have been able to prepare only
since 1883, would have appeared impossible and incompatible
with his causahty.

So there is no room in our causality for the idea of iron

PROBLEMS 167

with the specific gravity of air, or with one several times that of
gold. For, reasoning along the lines of our causality, we should
conclude that a substance that is so light or so heavy may,
indeed, exhibit chemical relationship with iron, but it would
not itself be sufficiently defined by the term iron.

Now Einstein also said : " Real Nature is much more
Umited (or bound) than our laws imply." A sceptic might be
disposed to take these statements separately in order to con-
strue a contradiction out of them. For, if there are limiting
conditions in Nature, which are foreign to the views expressed
in our laws, how would it then be possible for phenomena,
which cannot be imagined, to become reahzed ? If Nature
can do this, surely she must have more hberty than we seek
to impose on her. This apparent contradiction vanishes if
we treat the conception of structural design or uniformity as
something distinct from the measure of all experience up to
the present. This would give us the following interpretation :

Out of the manifold of occurrences that are possible in
mechanical Nature, real Nature selects a very closely defined
manifold. Thus the true laws imply a much greater degree of
hmitation than those known to us. For example, the laws
known to us at present would not be affected if we should dis-
cover electrons of arbitrary size or iron of arbitrary specific
weight. But Nature reahzes only electrons of a quite definite
size and iron of a definite specific weight.

Let us bear in mind that in aiming at ultimate truths we
have no final courts of appeal. Nor are the latter to be
assumed even when, in pursuing a theory, we encounter a
difficulty, which at first exhibits all the signs of a direct con-
ceptual contradiction. It should rather be realized that a
fiction containing an initial but only provisional contradiction
serves as a starting-point for just those investigations that are
most subtle and that have far-reaching consequences. We
should have no Infinitesimal Calculus, no Algebra, no Atomic
Theory, no Theory of Gravitation if, to avoid all initial con-
tradictions, we surrender the fiction of differentials, of imaginary
quantities, of the atom, of action at a distance. In short,
it may, indeed, be said that not only knowledge, but also fife,
the holding together of people by convention, law, and duty.

168 EINSTEIN THE SEARCHER

would become impossible if we did not accept the fiction
of free will, which directly contradicts the determinate char-
acter of all happening, including actions and motives, which,
physically, alone seems recognizable.

Fiction (not to be confused with hypothesis) and anthropo-
morphism, in spite of their inner inconsistency, are the two
poles about which our thoughts and our lives revolve. And
no doctrine will ever soar to such heights that it will be able
to deny completely its origin from these roots of all thought.
The Archin^edean thought-centre of the universe, which would
enable us to lift the world out of its hinges, is unattainable,
because it does not exist at all.

Is this also to apply to the new physics, whose results are
to be regarded as the last word in scientific knowledge ? Many
a hypercritical thinker might be led away by the current of
the preceding statement, and feel disposed to answer in the
affirmative, were it not that, here too, a contradiction intrudes
itself. This is expressed in the fact that not one of the present-
day philosophers is in a position to pursue the threads of this
theoretical fabric to their hidden ends.

Thus we arrive at a parting of the ways. Whoever aims
at becoming thoroughly famihar with Einstein's new world-
system finds that the study of the theory claims so much
attention that there is scarcely a possibility left of proceeding
to an ultimate philosophical analysis. And whoever is ab-
sorbed only by the desire of making philosophic investiga-
tions soon enough arrives at border-lines of thought, at which
his conscience warns him to beware of insufficient scientific
knowledge. He will be attacked by doubts as to whether he
has properly understood the theory. And he will be con-
fronted with the question whether he is justified in drawing
ultimate philosophical conclusions before he has mastered all
the mathematical details.

As far as can be judged at present, only one thinker has,
so far, had sufficiently wide knowledge to enable him to corre-
late the physical theory methodically with the theory of know-
ledge. I mean Professor Moritz Schlick of Rostock, who has
set out his ideas systematically in his book Erkenntnislehre,
which is extraordinary in itself and in its great scope ; it
takes us beyond Kant. In Schlick's opinion Einstein's theory

PROBLEMS 169

furnishes us with the key to new and unexpected chambers of
thought ; it is a wonderful instrument for opening up new
avenues, and would appear more wonderful still if we could
use this instrument without having recourse to anthropo-
morphism. This limitation may lead to a Utopia, or may en-
tail a circulus vitiosus. But we have one philosophy nowadays
which appHes to what cannot be fulfilled "as if " it really
is capable of fulfilment. Among the disciples of Vaihinger, the
founder of the As-If -doctrine of thought, we, however, notice
the tendency to follow anthropomorphic and fictitious paths
also in his field of thought.

From numerous utterances of Einstein, I have gathered
that he himself does not give his unqualified approval to all
attempts at unravelling the ultimate problems by means of
philosophy, that is, by using metaphysics alone. He does not
deprecate these endeavours, but even expresses admiration
for some of the newer works, as for that of SchHck, yet he sees
certain obstacles in the purely philosophical methods, that at
least restrain him from taking a systematic interest in them.
This reluctant acceptance of, and doubt in, the processes of
philosophy, that has never forsaken the exact investigator,
this suspicious attitude which scents traces of sophistic and
scholastic machinations in all metaphysical arguments, also
asserts itself in him in a noticeable form. He feels the absence
of rigour and of consistency of direction, which is a guarantee
of progress in passing from one result to another, in the method
of thought of those who are pure philosophers : and he de-
plores the spongy and murky appearance of certain ex-
pressions of thought, which, it must be admitted, form a poor
contrast to the completeness and the crystal clearness of
mathematico-physical reasoning. There was an inscription
on the portals of the Athenian Academy which stated that
entrance was forbidden to all who had had no mathematical
training ; we may imagine next to it an academy of pure
transcendental philosophy, bearing the inscription : No exact
research allowed ! I beheve that this clear-cut distinction
would tally with Einstein's view.

In the case of the great Ernst Mach, for whom Einstein
has intense admiration, we observe a similar attitude, or we
may say that, in the language of allegory, he sang openly the

ITO EINSTEIN THE SEARCHER

same refrain in another key. He never ceased reiterating that
he was properly ** no philosopher at all, but only an investigator
of Nature/' At the beginning of the introduction to one of
his works we read his confession : " Without in the slightest
degree being a philosopher, or even wishing to be one . . .** ;
and some Hnes further on he calls himself sarcastically " a
mere amateur sportsman " in philosophical regions. Yet,
Mach*s initial remark is followed by a remarkable result, for
the book in question, Knowledge and Error (Erkenntnis und
Irrtum), is to be reckoned among the most important works
in philosophical literature ; and he himself, the amateur
sportsman, who did not even desire to be called a philosopher,
accepted in 1895 the post of Professor of Philosophy at Vienna
University. It was merely his timidity in the face of the
philosophical fraternity that had made him emphasize re-
peatedly the distinction between his own work and that of the
philosophers, whereas in his heart he had nourished a passion
for Philosophy, the first mother of Science. And in my
opinion such a moment may arrive for even the most rigorous
investigator when he succumbs to the siren strains from
the shores of philosophy.

As far as Einstein himself is concerned, I cannot venture
on a prognostication. Even though he belongs to the category
and rank of Descartes, Pascal, d'Alembert, and Leibniz, in
whom Mathematics and speculative Philosophy are inter-
mingled, he is yet characterized by such a pronounced in-
dividuality, that it is quite inadmissible to draw conclusions
about him from others. He has no need to experience a day
of Damascus, for he carries the gospel of salvation in himself,
and it radiates from him. One thing seems possible, in my
opinion, namely, that Einstein will occasionally roam into the
neighbouring realm merely from aesthetic motives. Although
the means of philosophy are nebulous and more indefinite
than those of exact science, which are almost glaringly distinct,
philosophy itself for this reason is the more closely related to
Art. And a theory that applies to the whole universe must
assuredly contain many germs that may come to life if sub-
jected to the methods of Art. The connecting Unk between
Kant and Schiller shows in what sense this is to be understood.
Even at present there are indications in Art which tend to

PROBLEMS 171

show that it is ready to establish points of contact with
Knowledge. In France symphonic poems were written on
the measure relations of the circle, and on logarithms : these
are at present only curiosities, but may in future become
models. At a much later date, perhaps, the four-dimensional
universe may become ripe for treatment by such methods of
Art. On the way to this goal there is the treatment with the
symboUc, non-rigorous, and semi-poetic means of expression
used by Philosophy. Many will use their efforts to achieve
this, and perhaps they will come within closer range of success,
if Einstein himself lends a helping hand. It will not be
possible to arrive at new physical truths by following this
path, but those that are actually known will be traced more
readily to the great mainstream of philosophy. To fathom the
secrets of the world is the work of a recluse, but to make it
comprehensible to a wide circle, a preacher is necessary, who
uses the beautiful methods of philosophical rhetoric. Cosmos
denotes the World and its Ornamentation ; its creator,
Demiurge, is a master who fashions his forms along the lines
of Art.

Thus we have learned what Einstein regards as the sole
purpose of Science, namely, the search after Truth. For him,
the latter is something absolute in itself, and the possibility
of getting nearer to it is as great as the impossibility of de-
riving results of scientific use from, say, ethical discoveries.
For ethics is a field which is haunted by the conceptual
ghosts, and the manner of treatment, ordine geometrico, that
Spinoza wished to apply to it, is reserved for physics. Einstein
leaves the inverse philosophical query : "Is not Truth in
itself only something that we have constructed in imagina-
tion ? " to those who find pleasure in sauntering along paths
of thought that are totally unconnected, whereas he himself
advances in a straight line with the consciousness that even
if the goal is unattainable, he will at least not lose the right
direction !

CHAPTER VIII
HIGHWAYS AND BY-WAYS

Practical Aims of Science. — Pure Search for Truth. — Retrospective Con-
siderations.— The Practical Side of Kepler. — A Sajdng of Kant. — Mathe-
matics as a Criterion of Truth. — Deductive and Inductive Methods. — Con-
ceptual and Perceptual Knowledge. — Happiness and the Pleasures of Theory.
— Achievements of Science and Works [of Art. — Ethical Results. — Minor
Questions.

AGAIN we chanced to refer to the great subject : Can
or should theoretical science also pursue practical
aims ?
It is impossible to overrate the importance of this question.
It haunts us daily and often enough looms up threateningly
on the horizon of mankind. Observe what form the discus-
sions of educated people take when the finest and most sub-
lime achievements of mind are being debated : one talks of
the wonders of research in the remotest corners of astronomy
where the structures of world-wide star-systems are being
investigated ; we hear observations about the theories that
aim at tracing the cosmogonic development of universes from
the original chaos of countless ages ago. We hear mention
of exalted sciences, the Theory of Functions and Numbers,
whose founders and representatives are just as remarkable
in propounding problems as in solving them, and inevitably
the following question obtrudes itself : Of what use is it,
ultimately ? What can one do with it ? Can it be admitted
that theoretical science has an object of its own, or have we
at least the right to maintain the hope that, sooner or later, it
will bring us a real " UtiHty " expressible in practical terms ?
And just as the devotees of pure art have framed the
expression, " L'art pour Tart,'* so Einstein proclaims that
science is its own object, " Science for its own sake ! " It
carries its aims absolutely in itself and must not, through aim-

172

HIGHWAYS AND BY-WAYS 173

ing at other purposes, stray from its own highways. "It is
my inner conviction," said he, *' that the development of
science itself seeks in the main to satisfy the longing for pure
knowledge, which, psychologically, asserts itself as religious
feeling/'

" To yourself. Professor, the practical aspect seems com-
paratively insignificant ? "

" I did not say that, and it was not implied in the question.
We must not lose sight of our premises. As long as I am in-
terested in working along Unes of research — this was the
assumption — the practical aspect, that is, every practical
result that is found simultaneously or arises out of it later,
is a matter of complete indifference to me."

Far be it from me, even in thought, to wish to question this
confession of faith, particularly as the fact that it comes from a
searcher of the truth gives it the more weight. Yet a certain
uneasiness has crept over me because voices have recently
made themselves heard that demand for science a totally
different tendency. They arise not only from the pubUc at
large, but also from academic circles. Just a short time ago
I read an exposition by a well-known scientist, W. Wien,
in which he indulged in a violent polemic against the view
that purely scientific objects are alone valid. Professor Wien
addressed himself particularly to German physicists, reproach-
ing them with underestimating technical science, and with
regarding it as a " lowering of status " when a physicist enters
into practical life.

To this Einstein remarked : " I do not know at whom this
reproach is aimed, but I venture to think that my own atti-
tude can never have given rise to an attack of this kind. For I
make no divisions of rank, and recognize no higher and no
lower status. I affirm only what is the nature of science
herself, and the objects according to which she, objectively,
has to direct her gaze. Whatever further orientation in-
dividual investigators may seek for themselves depends on
the determining conditions of life of each, although these
conditions do not serve as a means for deducing the main
lines of research. The accusation that I am unwarranted in
putting forward this view will, I hope, not be levelled at me,
for my connexions with practice are manifold enough, and up

174 EINSTEIN THE SEARCHER

to the present moment I have often collaborated with practical
physicists. ..."

'' As I have regretfully observed when you were obhged
to interrupt a conversation with me to give an audience to
impatient persons seeking advice in technical matters ! "

" My own associations with the world of practice are not,
indeed, of recent date. My own parents originally wanted me
to become a technical scientist, and I was expected to choose
this profession to earn my livelihood. I was not, however,
sympathetically inclined to it, for even at an early age these
practical aims were to me, on the whole, indifferent and de-
pressing. My idea of human culture did not coincide with
the current view, that cultural development is to be measured
in terms of technical progress. Doubts, indeed, arose in me
as to whether technical improvements and advances would
actually contribute to the well-being of mankind. I must add
that, later, when I came into actual touch with technical
science, my opinion became somewhat modified, for the reason
that, here too, pleasures of theory often visited me."

The true position is probably that the technical worker
who does not merely think out improvements for machines,
but occupies himself with inventions on a higher plane, never
ceases to feel himself a theorist, since his achievements are
dependent for their inspiration on the fruits of theory. The
practical results of to-day are rooted in the theoretical results
of decades ago, and what is nowadays regarded as an idea of
pure research may in later decades acquire practical value.
Whether it actually becomes of value, or not, is of Httle account
in judging the idea. At any rate experience has shown that
the beginning of theoretical investigations hardly ever gives
us the chance of making prognostications. We spoke of the
discoveries of Volta, Ampere, and Faraday. When these
were first known, the world might have asked : Why have
they been disclosed ? To what can they be applied ? Of what
use are they ? Nowadays we know the answers that still
lay hidden at that time, and we proudly point to modern
dynamos. But does a dynamo really represent the significance
of these discoveries ? Would the importance and rank of
Volta, Ampere, and Faraday be less if the dynamo had not
come into existence ? Only an out-and-out materiaUst would

HIGHWAYS AND BY-WAYS 175

affirm this, and, strictly speaking, the question should not
even be raised. For it is in a sense equivalent to wishing to
judge of the importance and significance of the Polar Star
from its usefulness to the navigator on the earth's surface in
finding his bearings. We may put the question (although only
in the spirit of psychological curiosity, and without expect-
ing much elucidation) : Would these discoverers have been
particularly happy if they had divined the far-reaching conse-
quences of their work ? Did they, indeed, in the course of their
abstract researches, have a pre-vision of the future dominated
by the dynamo ? Einstein refused to answer this in the
decisive negative. He left room, if ever so little, for doubts —
that is, he considered that, in all probability, these three dis-
coverers had no presentiment of these consequences, and even
if they had in a dream caught a glimpse of our present electrical
age, their zest for discovery, their " pleasure in theory," could
scarcely have been increased ; for they were discoverers by
nature, who, swept along by their own spirits, did not need to
wait to satisfy the desires of practical application.

In Einstein's opinion, the presentiment that a discovery
may have practical applications in the future may react on
pure research. He quoted bacteriology as a proof of this.
In the series of eminent bacteriologists, ranging from Spallan-
zani to Schwann and Pasteur, there were certainly some
whose desire for knowledge was directed primarily towards
discovering purely scientific relationships. Pasteur himself
started from the theoretical question of the creation of life, that
is, from the problem of the origin of organic creatures from in-
organic matter without the medium of parent organisms. As a
pan-spermist he took up a negative attitude, that is, he tried
to prove that it is impossible to discover a bridge between
organic and inorganic matter. • Yet he doubtless knew that
his theoretical efforts stretched out into practical regions, and
he may easily have foreseen that they would exert a very
important influence on Medicine and Hygiene, although he
could not measure its full extent. In this case, then, we cannot
fail to recognize that a certain connexion between the desire
for pure knowledge and the impulse to apply it practically
is possible, serviceable, and justified in itself.

An influence in the opposite direction is also possible, and

1T« EINSTEIN THE SEARCHER

when, during the course of our conversation, we went in search
of examples, we came across one of great interest. It shows us
that a question may arise out of ordinary practice that may
open up an immense field of pure knowledge, nay, it may lead
to a science of very wide scope. As this example is not well
known, I shall mention it here ; I do so with additional
pleasure as the scientist involved is one of those whom Einstein
quotes most frequently and for whom he has the greatest
admiration, namely, Johannes Kepler. First we have the
surprising fact that Kepler, who, even when at the height of
his fame, was not free from care, was once the possessor of some
money. In the year 1615, his blessed year of fortune, the great
astronomer owned a comfortable home in Linz, and even dared
to conceive the idea of placing some well-filled casks in his
cellar; nay, more, he was in a position to publish a new scientific
work at his own expense, and thus appear as his own publisher.
This production of Kepler and his casks of wine are directly
connected, as we see clearly from the title : Doliometrie,
literally, " The Measurement of Casks." But the title of
the work gives not the slightest hint of its importance. For
these investigations relating to wine-casks actually became
the foundation of a science of sovereign power, the In-
finitesimal Calculus.

What was Kepler's aim ? It was something entirely
practical, and directed to a definite purpose, quite independent
of " pleasures of theory," to repeat Einstein's expression.
His problem was a question of economy, of using material
sparingly and appropriately, in accordance with the require-
ments of the careful head of a house. How must such a
cask be constructed from a minimum of wood to give the
greatest cubical content ?

His dehberations began by regarding wine as the precious
content enclosed by a figure in space, and then conceiving
the cask as representing a particular class of " bodies of
revolution," that is, of figures in space that may be regarded
as produced by the revolution of a curved fine about an axis.
At this point he at first endeavoured to gain a complete
survey of the question. He varied the boards along the
sides, the staves, and formed successively ninety-two such
bodies of revolution, some of which he named after the fruits

HIGHWAYS AND BY-WAYS 177

which they resembled in shape, as, for example, apple-shaped,
lemon-shaped, olive-shaped bodies. He started out by
measuring casks, and the final result was that his work,
Doliometrie, became the source of all future cubatures or
measurements of volume.

Now we come to the deciding point. What conditions
has the limiting surface of such a cask-like body of revolution
to fulfil, if the body is to have a maximum volume ? An
epochal discovery here came to hght. The practical head of
the house soars up into the sublime realms of the theory of
magnitudes. Kepler discovered the conception of changes
in functions, and their peculiarities at the maximum point.
(He did not, of course, use these modern terms.) By this
means, long before Newton and Leibniz, he laid the founda-
tions of Infinitesimal Calculus, which later became the heart
and soul of mathematics, of astronomy, of theoretical physics,
and of technical science, in so far as it is founded in mechanical
relations.

On the other hand, Einstein who now, three hundred years
later, has set up his differential equations, and, with them, a
new world-system, stands before us as a pure discoverer,
devoid of practical aims. But in these equations there are
elements of analysis that once came to light in a happy idyll.
This event did not come out of the grey obscurity of abstrac-
tion, but out of a region of earthly happiness, when a ray of
light found its way into Kepler's gloomy existence. No poet
has yet expressed this curious complex of events in a ballad,
telling how Truth, the only object of Science, was pressed out
of the grape, and how Practice, inspired by the inquiry of a
cooper, found its way to a Theory that stretches to the confines
of the Universe.

II

The conversation touched on famous expressions, words
carved in stone, in particular a saying of Kant which seeks
to fix the foundation and the hmits of knowledge. ** Every
science of Nature," the great philosopher of Konigsberg
had said, " contains just as much Truth as it contains mathe-
matics." And since, ultimately. Nature includes everything

12

178 EINSTEIN THE SEARCHER

— for a demarcation between physical and mental science no
longer seems possible — then, if we follow Kant, we should
have to regard mathematics as the sole measure of science.

It is certainly not yet possible to enter into a discussion
on this point with historians, medical or legal practitioners.
They would be justified in refusing it, since, in their subjects,
" truth " is not the sole factor, and because we cannot see at
present how the conception of a comprehensive mathematical
truth is to find a place in them. But when we question a
physicist on this point, who unceasingly uses mathematics
as his chief instrument, we should surely expect him to answer
with an unconditional affirmative. At least, I should not
have been surprised if Einstein had answered in this way,
and if he had indeed claimed its validity for every branch of
science.

But Einstein considered this quotation to be true only
conditionally, in that he accepted it as a principle, but did not
regard it as universal. That is, he does not recognize mathe-
matics as the only test of truth.

" The sovereignty of mathematics," said Einstein, " is
based on very simple assumptions ; it is rooted in the con-
ception of magnitude itself. Its dominant position is due to
the fact that it gives us much more delicate means of dis-
tinguishing between infinitely varied possibilities than any
other method of thought that expresses itself in language
and is restricted to the use of words. The greater the field
taken into consideration, the clearer does this become ; but
even in such a narrow range as i to loo, an estimate such
as 27 is incomparably more exact than can be expressed in
words in any other way. If we think of a series of sensations,
ranging from pleasure to pain, or from sweet to bitter, we
find that words leave us in an uncertain, confused state,
and we do not succeed in fixing on a point of the series with
the same precision as we above fixed on the 27 out of the 100.
But when the theory of magnitude plays a part in the question,
as, for example, in a series of tones, whose vibrations exhibit a
mathematical sequence, we immediately attain a much higher
order of precision by using numbers. ..."

That is why there is a sort of scientific pleasure in the
sequence of tones, so my thoughts ran on. Leibniz remarks

HIGHWAYS AND BY-WAYS 179

that " Music is the pleasure of the human soul, which arises
from counting without knowing that it is counting." Here
Pythagoras' ** Number is the essence of all things " is verified.
As soon as we arrive at the stage at which we feel the psycho-
logical essence of number, we fall into a sort of ecstasy,
because, in our subconscious minds, we experience not only
the pleasure of sense but also the underlying truth.

Einstein resumed : " Kant's remark is correct in the
sense that it sets up two things in clear contradiction to one
another. On the one hand, he has in view the fruits of know-
ledge of ordinary Hfe, in which our ordinary perceptions and
experiences are intermingled and cannot be disentangled by
inductive methods and deductive considerations. Opposed
to these, and to be regarded of higher rank, are the properly
scientific constructions — that is, such in which we find a neat
differentiation of connected thoughts that are based on regular
foundations and that form the links of a chain of deduction.
Whenever our science succeeds in detaching this logically
ordered knowledge from its sense-sources, it has a mathe-
matical character, and the amount of truth contained in it
will accordingly be determined by Kant's criterion. But Kant
demands too much when he asks us to apply this scale to all
attainable knowledge of science. It would seem advisable to
draw limitations if his remark is to serve as a regulative
measure. A great part of biological science will in future
still be obliged to make its way independently of purely mathe-
matical considerations."

" Your reflections, Professor, would then also apply to
the sajdng of GaUlei : The book of Nature Hes open before
us, but is written in letters other than those of our alphabet ;
its characters are composed of triangles, quadrilaterals, circles,
and spheres."

" With all due honour to the beauty of this observation, I
cannot refrain from doubting its universal validity. If we
were to accept it unconditionally we should have to regard
the paths of all research as purely mathematical, and this
would exclude certain very important possibilities, above all,
certain forms of intuition that have shown themselves to be
extremely fruitful. Thus, according to Galilei's interpreta-
tion, the book of Nature would have been illegible for Goethe,

180 EINSTEIN THE SEARCHER

for his spirit was entirely non-mathematical, indeed anti-
mathematical. But he possessed a particular form of intuition
that expressed itself as a feeling which put him into direct
contact with Nature, with the result that he obtained a clearer
vision than many an exact investigator."

" Do you then consider intuitive gifts to be separable at
all in form and in kind ? *'

" It would be pedantic to seek to estabhsh a fundamental
difference, even if we may regard the non-mathematical
intuition of Goethe as a very striking case. Moreover, as I
have often emphasized, all great achievements of science start
from intuitive knowledge, namely, in axioms, from which
deductions are then made. It is possible to arrive at such
axioms only if we gain a true survey of thought -complexes
that are not yet logically ordered ; so that, in general, intuition
is the necessary condition for the discovery of such axioms.
And it cannot be denied that, in the great majority of minds
with a mathematical tendency, this intuition exhibits itself as
a characteristic of their creative power."

" From these remarks it would appear that you value
deduction considerably higher than induction. Perhaps in
using these catchwords I am expressing myself a little vaguely ;
it seems to me that great things have been achieved, too, by
using inductive processes."

" Let us first define what each of these terms means.
Deduction is the derivation of the particular from the general,
whereas induction is the process of deriving the general from
the particular case. Now, quote any example of a brilliant
achievement, which you feel illustrates the power of the
inductive method. Of whatever kind your example may be,
you will soon become aware of the difference in the significance
of the two processes."

" For me the most perfect example of induction is given by
certain reasoning of EucKd. The question was whether there
is a finite or an infinite number of primes (that is, numbers
that cannot be divided without leaving a remainder except
by unity). EucHd found an elegant proof that the total
number is infinite by the following strictly inductive reasoning.
If the total number were finite there would have to be a
greatest prime. Let us call it w, and then form the product

HIGHWAYS AND BY-WAYS 181

of all primes up to n and including it, finally adding one,
thus: 2x3x5x7x11x13 . . . w, plus I. This new number,
say Y, is certainly greater than n, and now there are two
possibilities, either n is prime or it is not prime.

" If it is not prime, it must be divisible by some existing
prime. But the primes up to and including n cannot divide
exactly into Y, as there is always a remainder, namely, i.
Hence Y must be divisible by an existing prime X greater
than n. This contradicts the assumption that n is the greatest
prime, for^X is shown to be greater than n.

" Secondly, if Y is a prime, it immediately follows that n
cannot be the greatest prime, for Y is greater than n. Hence,
however great may be any prime that we may assume, there
will always be one that is greater, and even if we do not
succeed in expressing it in figures, we see that it must certainly
exist. Thus by studying carefully a particular case — the
prime n, which was assumed to be the greatest possible one —
we have arrived at a general theorem which states that there
is no Umit to the number of primes. Is not that, too, a triumph
of intuition ? "

" Certainly," said Einstein. " But you must not overlook
the fact that a theorem of this kind cannot be ranked with
a theorem of a fundamentally axiomatic character. The one
you have discussed has been derived by a clever process of
reasoning, but it does not exhibit the characteristic of a
momentous discovery. This theorem of EucHd can be im-
agined absent from science without the content of truth in
science being essentially effected. Compare with it a theorem
of axiomatic significance, such as Galilei's Law of Inertia, or
Newton's Law of Gravitation. Theorems such as the latter
are characterized by being starting-points of knowledge that
are inexhaustible in the consequences that may be deduced
from them. Your question, earher, as to whether I consider
the deductive method superior to the inductive, was not
formulated in correct terms. To this I answered above that
the inductive method as a means of discovering general truths
usually appears over-estimated. The proper form of the
question is : Which truths are of the higher order, those that
are found inductively, or those that lead to further deduction ?
There can scarcely be doubt about the answer."

182 EINSTEIN THE SEARCHER

" No, that is certainly true. If I understand your meaning
rightly, the answer may be expressed by an allegory. In-
tuition of the highest order creates treasure-mines, those of
lesser degree individual articles of value that are significant
in themselves, although they cannot be compared with the
inestimable value of the mines. The fact that the highest
intuition is found in minds with a mathematical trend makes
it appear possible that Kant's remark may gain more and
more credence in the future. It already apphes in a measure
to subjects to which it seemed inapplicable during Kant's
lifetime, for example, in Psychology, in which the relations
between stimulus and response have been established mathe-
matically only since the Weber-Fechner Law was set up ;
and also, since the time of Quetelet, in Moral Science and
Sociology, we learn from mathematical methods of statistics
and probability that even Man as an active being is subjected
to mechanical causality. At any rate it seems manifest that
Kant's remark, that in every science there is just as much
truth as there is mathematics, has received additional support
in recent times."

" That may be admitted," concluded Einstein, " without
recognizing his remark as an axiom. It is still far removed
from making possible unassailable deductions, and will never
quite succeed in doing so ; yet it may claim equal significance
as a beautifully expressed idea with that of Pythagoras, which
asserts number to be the nature of all things."

Ill

" The Unes of demarcation between ' conceptual know-
ledge ' (Erkennen) and * perceptual knowledge ' (Kennen) are
being drawn more and more closely nowadays. The former
is regarded as being the exclusive possession of the highly
developed human mind, and the latter as being characteristic
of the lower intelligence of other Uving creatures. Is this not
a pronounced case of anthropomorphism, and does it not
mislead us to form opinions that we should at once disown
if we succeed in stepping out^of our human frames even^for
a moment ? "

HIGHWAYS AND BY-WAYS 188

" We have to rest satisfied with anthropomorphism once
and for all," answered Einstein, " and there is no sense in
wishing to escape from it, for the arguments about anthropo-
morphism are necessarily also diffused with it, itself. We are
thus moving in a circle if we imagine we can deduce something
outside of human knowledge. As soon as we have argued
around the circle, we find ourselves again at the starting-
point, and so we are compelled to mark clear lines of division
between instinctive knowledge, derived directly by perception,
from conceptual knowledge, derived by processes of abstraction
and reflection ; in this way we award the palm of supremacy
to the human mind."

" But what if the following contradiction were to assert
itself ? Suppose that the logical ' circle ' is not a circle at
all, but a spiral, so that the final point of the argument lies
just a trifle above the initial point. I feel instinctively that
such apparently fruitless circuitous arguments might finally
lead to a definite piece of knowledge. For example, a certain
insect, the ichneumon-fly, although devoid of a knowledge of
science in our sense, infallibly plants its sting in a definite
point in the rings of a caterpillar, at just the point that serves
its purpose of paralysing the caterpillar without killing it.
It acts instinctively, and it is open to me to interpret this
occurrence in other words. The fly discloses that it * knows '
the anatomy of the foreign creature, although it has no con-
ceptual knowledge of it in our sense. But it immediately
follows from this analogy that, from the point of view of the
fly, its perceptual intelligence stands higher than our con-
ceptual intelligence — ^that is, by changing the perspective, I
am led to declare the anatomical knowledge of the fly to be
of higher rank than the analogous knowledge of the most
learned anatomist. In the same way I might persuade myself
that the mathematics of a bird of passage stands above the
cartographic knowledge of any human explorer. The migratory
bird that flies from the interior of Africa in a straight fine to
its nest in Mecklenburg must have something in the nature
of a co-ordinate system in its organism. The real reason that
we assign a higher position to our conceptual knowledge is
that we are equally proud of our intelligence as of our science ;
this is perhaps a deception depending on some compromise,

184 EINSTEIN THE SEARCHER

a sort of illicit deal in which the mind draws bills of exchange
on science, and, as a return, science meets its obligations by
paying in cheques drawn on the mind ! "

I must confess that these hazardous suggestions received
no welcome from Einstein, and were not even met with the
friendly smile with which he usually accompanies his refuta-
tions. Nor do I disguise from myself that the question of
conceptual or perceptual knowledge can in no way serve as
a basis of proof ; we may at most base certain conjectures
on the difference of these types of knowledge, conjectures
that suggest in words what eludes our clear comprehension.
Einstein's refusal to allow this possibiUty certainly rests on
much firmer groimd than the somewhat Bergsonian views
that I tried to present. Perhaps they are of a hair-splitting
nature, and deal with things Ijdng on different planes ; and
are deduced by unjustifiably altering the perspective with a
sort of sophistic somersault ; perhaps I may be reproached
with seeking, like Miinchhausen, to reach a higher standpoint
without having a support from which to start. Yet how is it
that I find it impossible to free myself from this chain of
thought ? No reason is forthcoming, for it is a purely meta-
physical question, and there has never yet been a clear system
of metaphysics free from ambiguities and sophism.

Let us rather confine ourselves to the conceptual inteUi-
gence characteristic of human beings, with which, according
to Einstein, so many pleasures of theory are available. I
asked him whether he would recognize differences of degree
in these pleasures, dependent on their intensities. Although
I rightly felt that he would answer in the affirmative, his
answer took a totally different turn from what I had expected.
It was, indeed, a great surprise, for in the matter of happiness
of spirit he expressed a view, according to which he — a great
discoverer ! — does not regard Science as the deepest source
of happiness !

" Personally," said Einstein, " I experience the greatest
degree of pleasure in getting contact with works of Art. They
furnish me with happy feehngs of an intensity such as I cannot
derive from other realms."

" This is indeed a remarkable revelation, Professor ! " I
exclaimed. " Not that I have ever doubted your receptivity

HIGHWAYS AND BY-WAYS 185

for products of art, for I have often enough observed how you
are affected by good music, and with what interest you yourself
practise music. But even at such moments when you gave
yourself up to the pleasures of the Muses, and were soaring in
regions far removed from the earth, I used to say to myself :
This is a delightful arabesque in Einstein's existence ; but I
should never have surmised that you regard this decorative
side-issue as the greatest source of happiness. But your con-
fession seems to go further, perhaps even beyond music ? "

" At the moment I was thinking particularly of Hterature."

" Do you mean literature in general ? Or had you a
definite writer in mind, when you were speaking of the
feUcitous effect of works of art ? "

" I meant it generally, but if you ask in whom I am most
interested at present, I must answer : Dostojewski ! " He
repeated the name several times with increasing emphasis.
And, as if to deal a mortal blow at every conceivable objection,
he added : " Dostojewski gives me more than any scientist,
more than Gauss ! "

** If, Professor," said I, after a pause that may easily be
accounted for — " if you mention in the same breath the names
of two such powerful but essentially different intellects, you
open the way to a discussion that cannot be settled by a mere
positive assertion. It is possible to admire intensely Dosto-
jewski as one who moulds personalities and who analyses the
inner struggles of the soul, and yet to deny him perpetual
fame. This depends on individual judgment, and, as for my
own, I believe that Dostojewski, in spite of his direct artistic
appeal, will not have his name perpetuated through the
centuries like that of many another member of Parnassus. It
seems to me to be a more important matter whether a common
measure can be found for Art and Discovery at all. Perhaps
the test of how far a work can be replaced may be regarded
as valid for each. When you say that Dostojewski gives you
more than Gauss, this probably corresponds with the feehng
that without Dostojewski you would have no ' Karamasoffs '
and hence would lack a certain life-value that cannot be
replaced. But if Gauss had failed to produce one of his funda-
mental theorems of Algebra, probably some other Gauss
would have appeared, who would have achieved this result.

186 EINSTEIN THE SEARCHER

According to this, then, our instinct increases the value of a
work of art, as we feel that we are dependent on one being
alone for its creation."

" But this is only to be admitted conditionally," said
Einstein, " for the best that Gauss has given us was likewise
an exclusive production. If he had not created his geometry
of surfaces, which served Riemann as a basis, it is scarcely
conceivable that anyone else would have discovered it. I
do not hesitate to confess that to a certain extent a similar
pleasure may be found by absorbing ourselves in questions
of pure geometry."

" Perhaps we may use a different characteristic as a means
of comparison," I suggested, " namely, the permanency of
the impression produced on the subject receiving it. For
example, a fine piece of music never loses its influence. We can
listen to the first movement of Beethoven's Ninth Symphony
a hundred times, and, although we know at every beat what
will follow, the state of pleasure continues unweakened ;
indeed, it might rather be said that the expectation of pleasure
increases from one hearing to the next."

*' This characteristic, too," answered Einstein, " cannot
be claimed as the exclusive property of works of art. Its
existence cannot be doubted, inasmuch as it belongs to every
eminent example of art. Yet we encounter it outside the
realm of art, too, in great advances of science, with which we
never cease occupjdng ourselves, and yet the impression con-
tinues unweakened."

" Do you include among them the impressions that a
discoverer experiences when he reviews in his mind the progress
due to his own efforts ? "

*' Naturally, and these, indeed, quite particularly ; and if
this question were put to me directly, I should answer un-
hesitatingly that I find pleasure in reflecting on my own
discoveries, and never experience feehngs of weariness in
passing over them again. So that, to return to our original
thesis, we must adopt a new basis of value if we wish to
account for the fact that the greatest degree of happiness is
to be expected of a work of art. It is the moral impression,
the feeling of elevation, that takes hold of me when the work
of art is presented. And I was thinking of these ethical

HIGHWAYS AND BY-WAYS 187

factors when I gave preference to Dostojewski's works. There
is no need for me to carry out a Hterary analysis, nor to enter
on a search for psychological subtleties, for all investigations
of this kind fail to penetrate to the heart of a work such as
" The Karamasoffs." This can be grasped only by means of
the feelings, that find satisfaction in passing through trying
and difficult circumstances, and that become intensified to ex-
ultation when the author offers the reader ethical satisfaction.
Yes, that is the right expression, ' ethical satisfaction ' ! I
can find no other words for it."

His whole face lit up, and I was deeply touched by his
expression. At that moment it seemed to me that he had
drawn the last veil from his soul ^ allow me to share in his
ecstasy. Was that the same physicist who interprets the
events of the world in terms of mathematics, and whose
equations encompass phenomena from electrons to universes ?
If so, it was a different soul ; one which gave utterance, like
that of Faust, to the words :

" And when in the feeling wholly blest thou art.
Call it then what thou wilt.
Call it Bliss ! Heart ! Love ! God !
I have no name for it !
Feeling is all in all !
Name is but sound and reek,
A mist round the glow of heaven I "

And, certainly, the book need not have been one of
Dostojewski's to excite this feeling in him. He chose the
latter to give expression to a mood that may change according
to what he reads, but undergoes no fluctuations in its ethical
foundation. From other occasions we know how little ethics,
that is conducted along systematic lines, signifies to him, and
that he does not even include it in the sciences. But at the
same time we see now that his inner life is dominated entirely by
the ethical principle. His deep love of Art is characterized by
it, and receives full satisfaction from the source of ethical joy of
which Art is the centre.

IV

During the autumn of 1918 Einstein was feeling indisposed,
and, on the advice of his doctor, did not leave his bed. When

188 EINSTEIN THE SEARCHER

I entered his room, I saw at once that there was no reason
for alarm, for pieces of paper covered with mysterious symbols
were lying about, and he was absorbed in making additions
to some of them. Nevertheless, I considered it my duty to
treat him as a patient under medical care, and did not conceal
my intention of leaving him after having inquired about his
condition. But he would not accept my visit as a mere call
to ascertain his progress towards recovery, and insisted that
I should remain with him a while, to converse about amusing
little problems as usual.

I pointed out to him that there were two objections to
this, the first being that he was unwell, and the second that I
was intruding on his work.

" How illogical 1" he answered. " If I interrupt my work
to chat with you, I am putting aside exactly what the doctor
would deny me if I were to allow him. So, let us make a
start. You have probably some conundrum weighing on your
mind."

" That may not be far wrong. I have been troubled by
something in connexion with Kepler's second law. It almost
robbed me of my night's sleep. My thoughts kept returning
to a certain question, and I should like to know whether there
is any sense in the question itself at all."

"Let us hear it ! "

" The law in question states that every planet in describing
its elliptic path, sweeps out with its radius vector equal
sectorial areas in equal intervals of time. But this seems
only half a law, for the radius vectors are only considered
drawn from the one focus of the ellipse, namely, the gravita-
tional centre. Now, another focus exists, that may be situated
in space somewhere, perhaps far away in totally empty regions,
if we assume the orbit to be very eccentric. My question is :
What form does this law take if the radius vectors are drawn
from this second focus and if the corresponding sectorial areas
are considered, instead of these quantities being referred to
the first focus exclusively ? "

" This question is not devoid of sense, but it serves no
useful purpose. It may be solved analytically, but would
probably lead to very complicated expressions, that would
be of no interest for celestial mechanics. For the second

HIGHWAYS AND BY-WAYS 189

focus is only a constructive addition, that has nothing
real in space corresponding to it. What else is troubling
you ? "

" My next difficulty is a little problem that sounds quite
simple and yet is sufficiently awkward to make one rack one's
brains. It was suggested to me by an engineer who certainly
has a keen mind for such things, and yet, as far as I could
judge, he did not get a solution for it. It concerns the position
of the hands of a clock."

** You surely are not referring to the children's puzzle
of how often and when both hands coincide in position ? "

" By no means. As I said just now, it is really quite per-
plexing. Let us assume the position of the hands at twelve
o'clock, when both hands coincide. If they are now inter-
changed, we still have a possible position of the hands, giving
an actual time. But, in another case, say, exactly six o'clock,
we get a false position of the hands, if we interchange them,
for on a normal clock it is impossible for the large hand to
be on the six whilst the small hand is on the twelve. The
question is now : When and how often are the two hands
situated so that when they are interchanged, the new position
gives a possible time on the clock ? "

" There, you see," said Einstein, " that is just the right
kind of distraction for an invalid. It is quite interesting, and
not too easy. But I am afraid the pleasure will not be of
great duration, for I already see a way to solve it."

Supporting himself on his elbow, he sketched a diagram
on a sheet of paper that gave a clear picture of the conditions
of the problem. I can no longer recollect how he arrived at
the terms of his equation. At any rate, the result soon came
to hand in a time not much longer than I had taken to enunciate
the problem to him. It was a so-called indeterminate (Dio-
phantic) equation between two unknowns, that was to be
satisfied by simple integers only. He showed that the desired
position of the hands was possible 143 times in 12 hours,
an equal interval separating each successive position ; that
is, starting from twelve o'clock, the two hands may be inter-
changed every 5 minutes xf ^ seconds, and yet give a possible
time.

190 EINSTEIN THE SEARCHER

I mention this little episode, which is insignificant in itself,
merely to give an example of how a great discoverer, too,
finds amusement in such distractions. In Einstein's case this
tendency to practise his ingenuity on unimportant trifles is
so much the more pronounced from the fact that he requires
an outlet for his virtuosity in calculation, and gratefully
welcomes every suggestion that helps him to reheve his mental
tension. Similar characteristics are reported of the great
Euler, as well as of Fermat, whereas many another eminent
mathematician feels decidedly unhappy if he drifts within
reach of the realm of actual numerical calculation. In my
mind's eye I still see Ernst Kummer, the splendid savant
(who, in his time, conferred distinction on Berlin University
by his very presence), suffering agonies whenever ordinary
arithmetical tables threatened to appear in the working-out of
his formulae. As a matter of fact, these two things, a mastery
over mathematics and a talent for ingenious calculation, are
to be considered as quite independent, even if we now and
then find them present in the same person.

In the case of Einstein this tendency is a symptom of an
incredible universality of spirit. It moreover presents itself
in the pleasant est forms, and a character-sketch of Einstein
would be incomplete if this trait were not mentioned. Every
problem which is in any way amusing excites in him a willing
interest and enthusiasm. I once directed our conversation
to the so-called Scherenschnitte. These are made from
long strips of paper or canvas, the ends of which are caused
to overlap a httle and then pasted together, but instead of
being fixed so that a flat wheel results, which rolls on one side
of the strip, the strip is twisted one or more times before the
ends are fastened together. If now the strip is cut lengthwise
right along its centre, various unexpected results occur, depend-
ing on the number of twists that have been made before pasting.

Some very complex geometrical difficulties are involved in
these problems. This is shown by the fact that learned
mathematicians have written extensive disquisitions on these
curious constructions (for example. Dr. Dingeldey's book,
published by Teubner, Leipzig). Einstein had never taken
notice of these wonders of the scissors, but when I began to
form these strips, to paste them, and to cut them, he immedi-

HIGHWAYS AND BY-WAYS 191

ately became interested in the underlying problem, and pre-
dicted in a flash what puzzling chain constructions would
result in each case, with a certainty that would lead one to
imagine that he had spent days at it. On another occasion
a space-problem dealing with dress came up for discussion :
Can a properly dressed man divest himself of his waistcoat
without first taking off his coat ? One would not have dared
to confront Copernicus or Laplace with such a problem.
Einstein at once attacked it with enthusiasm, as if it were an
exercise in mechanics, the body being the object ; he solved it
in a trice, practically, with a Httle energetic manipulation,
much to the amazement and joy of the beholder, who asked
himself : Is this the same Einstein who developed the work
of Copernicus and Newton ? A Uttle later, perhaps, the con-
versation centres around some serious point drawn from
pohtics, poUtical economy, sociology, or jurisprudence. What-
ever it may be, he knows how to spin out the suggested thread,
to establish contact with his partner in conversation, to open
up his own perspectives without ever insisting on his point
of view, always stimulating and showing a ready sympathy
for the subject of discussion and for all the ideas which it
crystallizes, the prototype of the scientist, in the mouth of
whom Terence put the words : " I am a human being ; nothing
that is human is alien to me ! "

CHAPTER IX
AN EXPERIMENTAL ANALOGY

Forms of Physical Laws. — Aids to Understanding. — Popular Descriptions.
— Optical Signals. — Simultaneity. — Experiments in Similes.

I WISH to ask you, Professor, to help me over a difficulty
and to treat me as the spokesman of a great number
who are similarly troubled. In most accounts of your
theory of relativity, there is a dearth of definite, concrete,
illustrative examples on which we can fix our minds whenever
the theorem is to be appHed generally without hmitation.
Let me express this more precisely : Your simplified picture
of the structure of the universe is achieved in the theory of
relativity by emancipating all observations from fixed co-
ordinate systems, and by proclaiming the equivalence of all
systems of reference. One of your earHest theorems states
that physical laws describing how the states of physical
systems alter, remain the same, no matter to which of two
co-ordinate systems these states are referred, provided that
the co-ordinate systems are moving rectilinearly and uniformly
relatively to one another. This theorem entails the following
statement. If we — erroneously — ^adopt a non-relativistic view,
we shall come to the conclusion that physical laws depend on
the particular system of reference chosen, and will thus assume
a different form for each different system. At this point we
experience a desire to hear definite examples. What varying
forms may a certain given physical law, known under a definite
form, assume, and how can we use this law to show that it
must adapt itself to the postulate of relativity ? "

Einstein explained that such examples cannot be given
in special cases, but only in very general terms. If we were
to suggest the elliptic orbits of the planets (at which I had

192

AN EXPERIMENTAL ANALOGY 193

hinted in my remarks), we should fall into error, for the law
of elliptic orbits is no such law. For, from another point of
view, the elliptic paths of the planets might be drawn out into
wavy Hues, or into spirals, and they would remain ellipses
only as long as the lines of motion are referred to the central
attracting body. But the constancy of the velocity of light
is such a law, as also is the law of inertia, according to which
a body that is left to itself moves uniformly in a straight line.
I confessed to him that this limitation to a few very general
laws would be a painful matter for many an enthusiast of
average attainments, who has great difficulty in distinguishing
the laws that are generally valid from those that hold only
within circumscribed limits. But if this were not so, we should
have to alter our conception of what is conveyed by a popular
exposition. For it is called popular, not because it now and
then uses the patronizing words " dear reader," but because
it anticipates the questions and doubts of the man of average
sense, and examines them, proving some to be unjustified
and others to be reasonable or unreasonable, as the case may
be. '*Then there is a further matter that troubles me," I
continued. " Let us suppose an ordinary reader of such a
popular account to get a first insight into the new conception
of Time. He is glad to feel the ideas dawning in him, and, to
get a more lasting view of the idea, he repeats the arguments
through which he has just threaded his way, and, in doing so,
again encounters the phrase ' uniform motion.' At the first
reading he imagined that he understood the expression quite
well, but the second time he pauses and considers. For now
that he knows how much depends on it, he is anxious to find
out the exact meaning of a ' uniform motion.' He looks for a
definition, and if he cannot find one in the book he is perusing,
he endeavours to reason it out for himself. With good luck
he arrives at the usual statement : a body moves with ' uni-
form motion ' if it traverses equal distances in equal intervals
of time. But equal intervals of time are clearly those during
which a body in uniform motion traverses equal distances.
In other words, he explains A by means of B, and B by means
of A, so that he has involved himself in a vicious circle from
which he cannot escape. This is his hour of need, due to the
difficulty of * time.'
13

194 EINSTEIN THE SEARCHER

" He hopes that further study will remove this obstacle.
He meets with the conception of ' simultaneity,' which is
defined for him anew, and is disclosed as being ' relative.*
He manoeuvres further towards the fundamental theorem that
every body of reference has its own particular time.

" His popular booklet makes this clear to him by quoting
the example of a fi3dng-machine, or, better still, a railway train
that is nishing along an embankment at a very great speed,
and that carries a passenger. Two strokes of lightning I and II
are to take place at two widely distant points on the embank-
ment. The question is then : When are these two flashes
of lightning to be considered * simultaneous ' ? What
conditions must be fulfilled to ensure this ? It is found —
incontrovertibly — ^that the light -rays starting out from the
two strokes of lightning must meet at the mid-point of the
embankment.

" It now follows from a short chain of argument that the
observer in the train will see flash II earlier than flash I,
if they reach the observer, who is at rest, at the same moment.
That is, two events that are simultaneous with respect to the
embankment are not simultaneous for a moving system (such
as a train or a flying-machine) ; the converse is, of course,
also true.

" Here, again, the eager layman encounters difficulty, for
he asks himself : Why should the two events be characterized
or defined by lightning-flashes in particular ? If acoustic
signals were used instead, nothing would be altered in the
fundamental determination, for the sound rays (sound-waves)
would likewise meet at the mid-point of the Hne joining the
sources of disturbance. What is the reason that the relativity
of time arises only when phenomena are regarded optically,
and that rays of light play the deciding part in all later develop-
ments ?

*' And this particular query is followed by one which is more
general : Why does the popular pamphlet not read this question
in my mind ? I know that the author of it is more skilled in
these matters than I, but just this superiority should help him
to divine what is passing in my mind when I make efforts to
follow his reasoning."

Einstein had listened to me patiently, and then he explained

AN EXPERIMENTAL ANALOGY 195

to me at considerable length why in this case optical signals
cannot be replaced by sound signals : light is the only mode of
motion that shows itself to be entirely independent of the
carrier of the motion, of the transmitting medium. Thus the
constancy of velocity is assumed in the above argument, and
as this constancy is an exclusive property of light, every other
method must be discarded as unallowable for investigating
the conception " simultaneity." Furthermore, he showed me
how, on the basis of relativity, starting from the embankment -
experiment, we may arrive at a perfectly consistent representa-
tion of the conception of Time. He certainly did this by
applying subtle physical arguments that exceed the scope of
the present book.* He added, in substance, that it was
futile and impossible to discuss in detail all the conceivable
objections that might arise in the mind of one reading a popular
work of this kind : it was a futile undertaking, because the
true purpose was defeated, inasmuch as a clear development
of the fundamental thought would be almost impossible under
the cross-fire of so many random questions.

Thus, in this matter, Einstein takes the same stand as
Schopenhauer in the preface of his chief work, in which he
says : ** To understand this work no better way can be advised
than to read it twice (at least), inasmuch as the beginning
assumes the end, almost as much as the end assumes the
beginning ; the smallest part cannot be understood if the
whole has not already been understood." Whoever accepts
and follows this advice will find that the intermediate objec-
tions will gradually balance and cancel one another, and that
it is not necessary that they should interrupt the steady and
consistent line of development.

The position would be different if a disciple of the new
theory should resolve to dispense with strictly scientific reason-
ing altogether, and should wish to meet the wishes of his
readers or hearers by discarding accuracy entirely. Such a
programme seems quite feasible.

• In these arguments, arrangements of synchronous clocks occur, which
are fixed into the co-ordinate systems, the positions of their hands being
compared with one another. The " time " of an event is then defined as
the position of the hands of a clock immediately adjacent to the scene of the
event.

196 EINSTEIN THE SEARCHER

" This would be merely following the sketchy method of a
magazine," Einstein remarked, " but you do not seriously
think that it would lead to anything ? "

" It would not be a true explanation, which is reserved for
technical productions. But I can imagine that it would not
be unprofitable to help one who is entirely ignorant on these
questions by using makeshifts, in the form of allegories or
analogies, which will serve as supports if he should take fright
during the course of his earlier studies. These shocks are
bound to occur, as, for instance, when he learns that a moving
rigid rod undergoes contraction in the direction of motion."

" But this is proved to him ! "

" Nevertheless, he does not easily accept it. For the
general reader will say to himseK : * A superhuman effort is
imposed on my mind. A rigid rod is the most constant of all
things, and never before has one been compelled to regard
something that is constant as variable.' "

" If he does not grasp it, no analogy will teach him."

" But perhaps it is possible. The analogy is to show him
that the effort is not superhuman, and that thinking Man has
already had occasion to become familiar with such trans-
formations from constant to variable factors."

*' I am afraid your analogy will prove a failure."

** From the scientific point of view this is probably true,
inasmuch as all comparisons are imperfect, but the analogy
may yet be of service as a last resort. For example, I should
say to my general reader : ' Picture to yourself a savant of the
Middle Ages who reflects on the constitution of animals and
plants. One fact seems to him to be irrevocably true, namely,
that the species are unchangeable ! A palm tree is a palm
tree, a horse is a horse, a worm a worm, and what is once a
reptile remains a reptile. A species in itself denotes something
absolutely invariant."

" The expression is wrong when taken in this connexion ;
you mean invariable."

" A little inaccuracy more or less does not affect the
analogy. For the sake of my picture I should like to retain
the conception-couple, variable and invariant. Well, then,
the species give our savant the impression of in variance, as
in the view that was held by Linn^ and Cuvier. This view

AN EXPERIMENTAL ANALOGY 197

necessarily has its counterpart in his thought. He argues
that every species has its own original root, and that, in this
sense, there is very extensive variation. The fundamental
roots are extremely manifold ; Nature has produced in-
numerable variations in her individual acts of creation. But
now the Theory of Descent of Lamarck, Goethe, Oken, Geoffroy
St. Hilaire, enters the field and produces a complete inversion
of these two elements ; the two parts of the earlier point of
view change places. Our savant has to revise his whole world
of thought. Now all organisms are to be traced back to a
single original root : the latter, which was variable before,
becomes an invariable unicellular primitive organism, but the
apparently unchangeable species now becomes variable, in the
widest possible sense. And even if this savant should ex-
claim : ' How am I to reconcile myself to this view ? ' his
descendants later find no difficulty in accepting the idea that
the organic roots are uniform, and that it is the species that
are subject to all manner of variation as a compensating
feature."

Einstein expressed himself very little pleased with this
attempt at an analogy, and found that it was so far fetched
that it could not be considered admissible.

'* Then I must ask your permission to continue my at-
tempt ; perhaps something useful may yet result from it.
I now picture to myself a human being who lived in classical
times and who, following Ovid and the great majority of his
contemporaries, regards the earth as a disc. On this disc,
each inhabitant of the earth has his own particular position,
for the disc has a centre with reference to which the position
of a person can be specified if his distance and his angular
displacement from a given initial radius is specified. Thus,
there is a variation of position if various persons are considered.
On the other hand, the Above and the Below is absolutely
invariable for all persons, for the lines running between Above
and Below are all parallel for them, since they all have uni-
formly the same disc under their feet and the same heaven
above their heads. Ovid would therefore have refused to
entertain for a moment the suggestion that Above-Below is a
variable. But his distant descendants accepted the view that
the earth is spherical and that there are antipodes as self-

198 EINSTEIN THE SEARCHER

evident, and they found not the sHghtest difficulty in
considering the Hne Above-Below to vary with their own
position, making all possible angles with an initial line extend-
ing to direct oppositeness. Referred to the centre of the sphere,
all people have how an ' invariant ' position, whereas, in
compensation, the Above-Below is subject to every conceivable
variation. And now I again address myself to the average
reader, and say that the meaning of these analogies is that
every doctrine that leads to a great uniformity converts what
was formerly invariant into a variable quantity, and vice
versa. The theory of relativity makes all considerations about
the physical world independent of all co-ordinate systems ;
it establishes completel}^ invariable uniformity, removed from
all changes due to varying points of view. Hence what was
previously invariable — such as a rigid measuring-rod — will
now become variable. It is not surprising that this requires
a new method of thought, a revision of our mode of reasoning,
for the above analogies show that these radical adjustments
are characteristically necessary in the case of comprehensive
theories, and that such theories are able to overcome appar-
ently firmly established ideas. The parallels that I drew
above will at least inspire the average reader with a certain
confidence, for they show him how results of reasoning that
were once considered incredible were regarded as self-evident
by later generations."

I have already emphasized sufficiently that Einstein
regards as inadequate these auxiliary pictures that have
presented themselves to me. Yet in the course of the conversa-
tion I gained the impression that his judgment grew somewhat
milder, and that, with certain reservations, he was disposed
to let them pass as tolerably useful helps — and they are not
intended to be more than this. I think, therefore, that I
am not acting counter to his wishes in citing these allegorical
examples here, particularly as they arose in the course of our
talks.

Since then, I have had many opportunities of testing these
examples on certain persons, and may mention that they
proved quite useful. Analogies of this kind may offer a
friendly help in moments when the uninitiated feel themselves
in peril, and encounter a difficulty which they imagine to be

AN EXPERIMENTAL ANALOGY 199

insurmountable. They do not remove the difficulty, but they
impart a certain power of expansion to the intellect and
encourage a continuation of effort, which would probably
otherwise be relaxed at the first sign of something which is
imagined to be inconceivable. There is thus no room in
textbooks for such helps, but they may justifiably find a
place in a book that departs from the methodical route, and
hopes to discover in by-ways things that are suggestive and
instructive.

CHAPTER X
DISCONNECTED SUGGESTIONS

Conditionality and UnconditionaJity of Physical Laws. — Conception of
Temperature. — Grain of Sand and Universe. — Are Laws unalterable ? —
Paradoxes of Science. — Rejuvenation by Motion. — Gain of a Second. —
Deformed Worlds. — Atomic Model. — Researches of Rutherford and Niels
Bohr. — Microcosmos and Macrocosmos. — Brief Statement of the Principle
of Relativity. — Science with reduced Sense-Organs. — Eternal Repetition. —
Higher Types of Culture.

IN all branches of reasoning, no word and no conception
has played a more important part than that of law.
Physical laws denote the barrier that separates strictly
chance and arbitrariness from necessity, and it seems to us
that the region of the latter must ever extend so that finally
nothing will be left of the former, which will have become
amalgamated with necessity. We shall be constrained to
believe more and more in a supreme law that will be a com-
plete expression of all the partial laws which science presents
to us as more or less permanent results of individual researches.

Our conversation was centred about these individual laws,
such as those that are taught in the theory of gases, optics,
etc., and that are associated with the names, Boyle, Gay-
Lussac, Dalton, Mariotte, Huyghens, Fresnel, Kirchhoff,
Boltzmann, and others. In connexion with these I asked
Einstein whether he regarded the laws as things unconditioned
in themselves, and capable of proof under every set of circum-
stances ; and whether absolutely valid laws existed or could
exist.

Einstein's answer was essentially in the negative. " A
law cannot be final, if only for the reason that the conceptions,
which we use to formulate it, show themselves to be imperfect
or insufiicient as science progresses. Let us consider, for

200

DISCONNECTED SUGGESTIONS 201

example, an elementary law such as Newton's Law of Force.
From our more recent point of view we find the conception
of direct action at a distance to be inexact in Nature. For
it has been shown that action at a distance is not an ultimate
factor, but must be resolved into a multiplicity of actions
between immediately neighbouring points (The Theory of
Action by Contact or Contiguous Action). Another example
is provided by the conception Temperature. This conception
becomes meaningless if we endeavour to apply it to molecules :
it leads to no result if we try to impose it on the smallest parts
of matter as such. The reason is that the state, the velocity,
and the inner energy of the individual molecules fluctuates
between very wide limits. The conception * temperature '
is applicable only to a configuration composed of many mole-
cules, and evep then it is not applicable quite generally. For
let us picture to ourselves an extremely rarefied gas contained
in a closed receiver. Two opposite walls are to be at different
temperatures, the one being cold and the other being hot
In a gas at such very low pressure the molecules come into
collision so seldom that, practically, we have to take into
account only the collisions of the molecules with the confining
walls. The molecules that rebound from the hot wall have
greater velocities than those coming from the colder wall, and
hence the conception of temperature becomes untenable for
this gas."

" Would the temperature-scale on the thermometer then
denote nothing ? " I asked. " The greater or lesser degree of
warmth of a body, in this case of the mass of gas, depends on
the more rapid or less rapid motion of its smallest parts. The
motions are in any case present, so what would a thermometer
indicate ? "

" It would betray only that it had nothing to indicate.
If a thermometer that is blackened on one side were inserted
into the vessel containing the gas, then different temperatures
would be recorded if the thermometer were gradually turned
about its own axis ; and this signifies that the conception of
temperature has become meaningless for this configuration
of molecules. And passing beyond the quoted examples, I
should maintain that all our conceptions, however subtly they
may have been thought out, are shown in the coiirse of pro-

202 EINSTEIN THE SEARCHER

gressive knowledge to be too rough hewn, that is, too little
differentiated."

We spoke of the " Properties of Things/' and of the degree
to which these properties could be investigated. As an
extreme thought, the following question was proposed :

Supposing it were possible to discover all the properties
of a grain of sand, would we then have gained a complete
knowledge of the whole universe ? Would there then remain
no unsolved component of our comprehension of the universe ?

Einstein declared that this question was to be answered
with an unconditional affirmative. " For if we had completely
and in a scientific sense learned the processes in the grain of
sand, this would have been possible only on the basis of an
exact knowledge of the laws of mechanical events in time and
space. These laws, differential equations, would be the most
general laws of the universe, from which the quintessence of all
other events would have to be deducible."

[This thought may be spun out in yet another direction.
Every piece of research, however specialized it may appear
and of whatever minor importance it may be, retains a relation-
ship with researches into the universe, and may prove to be
valuable for this latter task. If we accept the view that
science is capable of realizing perfection, then every con-
tribution to knowledge, even the most insignificant, is essenti-
ally indispensable for attaining this goal.]

Can a physical law alter with time ? In more precise
language, can time, as such, enter expUcitly into laws, so that,
for example, an experiment that is carried out at different
times leads to different results ? This question has been
treated several times, among others, by Poincare, who answered
it with an emphatic " No ! " but also by others to whom the
invariability of physical laws did not seem to hold for all
eternity. If my memory does not play me false, Helmholtz
once expressed faint doubts about the constancy of laws.

Einstein answered this question with a decided negative.
" For a law of physical nature is, by definition, a rule to which
events conform wherever and whenever they take place.
Thus, if we were to be compelled as a result of experience to

DISCONNECTED SUGGESTIONS 203

make a law dependent on time, it would be a necessary step
to seek a law independent of time, which would include in
itself the law dependent on the time as a special case. The
latter would be excluded from the category of physical laws,
and would henceforward play the part only of a result deduced
from the law which is independent of the time."

What attitude should we adopt if, in stud3dng a scientific
doctrine, we encounter paradoxical results even though the
inferences have been drawn correctly — ^that is, if we meet
with a deduction to which our reasoning powers object,
although no fallacy is discoverable in the argument ?

Before we deal with cases which seem to me, personally,
to be interesting, let us hear what is Einstein's attitude in
general. " As soon as a paradox presents itself, we may, as a
rule, infer that inaccurate reasoning is the cause, and should
thus examine in each particular case whether an error of
logic is discoverable, or whether the paradoxical result denotes
only a violent contrast with our present views."

Let us first take examples from an entirely modern science,
from the Theory of Aggregates founded by Georg Cantor of
Halle. We shall follow the argument by the only possible
method for this book, namely, by rough indications that will
serve our purpose and do not claim to be accurate in expression
or in sense.

If we take an aggregate of three objects, for example, an
apple, a pear, and a plum, we may, by definition, form six
partial aggregates, namely :

the apple

the peax

the plum

the apple and the pear

the apple and the plum

the pear and the plum.

The aggregate of the partial aggregates, which contains
six elements, is thus greater than (actually twice as great
as) the original aggregate, in which only three elements
occur.

If the original aggregate contains an additional element.

204 EINSTEIN THE SEARCHER

for example, a nut, the following partial aggregates may be
formed :

the apple

the pear

the plum

the nut

the apple and the pear

the apple and the plum

the apple and the nut

the pear and the plum

the pear and the nut

the plum and the nut

the apple, the pear, and the plum

the apple, the pear, and the nut

the apple, the plum, and the nut

the pear, the plum, and the nut.

Thus, in this case, the aggregate of the partial aggregates is
already considerably greater than the original aggregate. This
numerical excess increases rapidly with each successive increase
in the original aggregate, so that if we apply the same reason-
ing to an infinite aggregate, the aggregate of partial aggregates
becomes an infinity of a higher order. This is expressed by
saying that the infinite aggregate of partial aggregates has a
greater potentiality than the infinity of the elements of the
original aggregate.

So we see that the one infinity is, in popular language,
much more comprehensive, more powerful than the other.
Our minds do not find it impossible to grasp this. But in a
definite imaginary experiment it is found that this theorem
of progression not only fails in its application, but leads to
flagrant contradiction.

For if we start from the primary aggregate of " all con-
ceivable things, *' its infinity can certainly not be transcended
by any other infinity. But according to the above theorem
the " aggregate of all partial aggregates " would have a greater
potentiality, although it itself cannot extend further than
to the conception of the maximum of all conceivable things.
We thus arrive at an insoluble paradox, a typical example of
how, in the system of conceptions involved, something is
insufficient or not in conformity with logical thought. And
this sceptical view receives support from various remarks of
Descartes, Locke, Leibniz, and particularly Gauss, who, long

DISCONNECTED SUGGESTIONS 205

before the advent of the Theory of Aggregates, raised a protest
against inexact definitions of infinity.

In another case, however, the same theory seems to arise
by perfectly logical processes, although it again leads to a
statement that does not seem correct to " common sense/'
For it shows by a very subtle and ingenious method that all
the surface-points of a surface infinitely extended in all direc-
tions may be brought to correspond in a reversible single
manner to the linear points of a Hne, however small ; so that
to every point of the unlimited plane there corresponds a
definite point of the line, and vice versa. The same theorem
may be extended to three-dimensional space, with the result
that we have to reconcile ourselves with the incredible fact
that, expressed in popular language, a straight line of however
small length exhibits the same potentiality with regard to the
number of its points, as all the points in the universe.

For my own part, I must confess that no means suggests
itself to me to make this paradox inteUigible. But the sacri-
ficium intellectus comes within dangerous proximity. Einstein,
who values and marvels at the theory of aggregates as a science,
or perhaps more as a work of art built up from the materials of
science, gives whole-hearted support to the proof. He refuses
to accept the notion of a paradox — ^that is, he recognizes a
contradiction not in our process of reasoning, but only in a
habit of thought that is open to correction, I should give
much to discover the means of correction !

A third example arises out of the special theory of rela-
tivity. It has a mysterious paradoxical character that
vanishes when a clear view of the relationships involved has
been obtained.

According to this theory the rate at which events happen
alters according to the state of motion of the system under
consideration. Let us now consider two twins A and B,
that, although born at one place on the earth, are immediately
separated, B remaining at rest, whilst A rushes out into space
at an enormous rate, describing what, viewed from the earth,
is an inconceivably great circle. In this way the rate of
happening of all events is reduced very considerably for A
in a manner that may be calculated. If A then returns to

206 EINSTEIN THE SEARCHER

B, it may happen that the twin who stayed at home is now
sixty years old, whereas the wanderer is only fifteen years of
age, or is perhaps only an infant still.

The first introduction to this flight of imagination naturally
causes profound perplexity. Nevertheless, we are deaHng not
with a realm of miracles, but with something that is within
the range of comprehension.

" In the case of these two twins," Einstein declared, " we
have merely a paradox of feeling. It would be a paradox of
thought only if no sufficient ground could be suggested for the
behaviour of these two creatures. This ground, which accounts
for the comparative youth of A, is given, from the point of
view of the special theory of relativity, by the fact that the
creature in question, and only this creature, has been subject
to accelerations. A proper grasp of the reason is furnished
only when we adopt the general theory of relativity, which
tell us that, from the point of view of A, a centrifugal field
exists, whereas it is absent from the point of view of B. This
field exerts an influence on the relative rate of happening of
the events of life."

It certainly requires a prodigious mechanism to allow
the moving twin to gain even only one second of time. If he
were to spend a year in a merry-go-round whose circumference
were about 19 milUard miles in length, he would have to
travel in it at the rate of over 600 miles per second if he is to
gain a second on his brother.

This inevitable result that is immediately apparent to a
trained scientific mind throws fight on the nature of " common
sense," the validity of which, as an ultimate criterion, Kant
too has refused to recognize, in so far as this " common sense "
is incapable of passing beyond the examples offered in its own
experience. It circulates, as Einstein says, in the " realms
of feeling and analogy." It finds no analogy for a phenomenon
like that described above, and since it can apply rules only
concretely, many things appear to it paradoxical that, in the
light of intensified abstraction, appear logical and necessary.

Let us speculate on the following question. If all things
in the universe should increase or decrease enormously in
dimensions, and if, at the same time, in a manner totally

DISCONNECTED SUGGESTIONS 207

concealed from us, certain physical conditions should become
changed, we should lack all means of discovering the difference
between things before and after the change. For since all
measuring-rods, including those furnished by our senses, would
have become changed in the same proportion, the two condi-
tions could not be differentiated from one another. It may
easily be shown that this would necessarily occur, if an extra-
mundane power were non-uniformly to displace, deform,
compress, or bend all things in the universe, provided that our
instruments and senses participated in this transformation.
Accordingly it is permissible also to regard the universe known
to us as one that is deformed, and one that is derived from
another, the original form of which will ever remain a secret
to us.

Is there any connexion between this grotesque speculation
and the theory of relativity ?

We can establish only one that is negative and that arises
e contrario. ** These deformations," said Einstein, " are in
themselves abstractions that are physically meaningless. Only
relations between bodies have a physical meaning, for example,
the relation between measuring-rods and the objects they
measure. Therefore, it is reasonable to talk of deformations
only when we are dealing with the deformations of two or
more bodies with respect to one another, whereas the con-
ception of deformation has no sense, unless a real object is
specified, to which it is referred. The philosophical merit of
the general theory of relativity, as compared with previous
views of physics, consists in the fact that the former avoids
entirely these meaningless abstractions with respect to space
and time."

[According to this, it is not purposeless to enter on these
grotesque trains of thought, even if they are untenable physi-
cally. For since the new physics teaches us to avoid these
false tracks, it seems of value to know what it is that is to be
avoided. Just as we must study scholastic thought if we
wish to grasp thoroughly the philosophy which sprang up after
the scholastic fetters were burst. Moreover, these reflections
on concealed universes are not without a certain attraction,
reminiscent of the sorcerer's wand, if they pursued any other
goal than that of making universes distorted. It is true that

208 EINSTEIN THE SEARCHER

they hold out latent temptations that may in some cases lead
us on to dangerous ground, in encouraging us to venture on
analogies beyond the scope of geometry and physics. Would
it be possible to enter suddenly into a world that is distorted
and deformed with respect to its ethics, its culture, and its
reasoning intellects, without our observing the difference ?
Are we ourselves perhaps Hving under such deranged conditions,
of which we cannot become aware, because our perceptual
organs have likewise become deformed ? I must frankly
confess that I do not regard it as quite inconceivable that
this argument of deformation may be spun out in this direction,
but I must add that Einstein rejects absolutely all such exten-
sions, since, as he emphasizes, they lead to regions that are
merely fields for the exhibition of " verbal gymucistics."]

The question whether Nature makes leaps or not is very
old. In the theory of descent it forms the foundation of the
difference between revolutionists and the evolutionists, who
uphold the axiom natura non facit saltus, with all its conse-
quences. Recently attempts have been made, particularly by
psychologists, to propound and justify a natural principle of
discontinuity. They assert that our own perceptions and
sensations are discontinuous in themselves, and that the
mechanism of every perception is akin to that of a cinemato-
graph with its extremely rapid interruptions. If this should
actually be the case, we should scarcely have a means of solving
definitely the question whether continuity reigns, or not, in
Nature.

Einstein does not recognize the possibility of this alternative
for a moment. If a doubt had ever arisen, the researches of
Maxwell would in themselves have been sufficient to dispel it.
Our universe that is to be described in terms of differential
equations is absolutely continuous.

" But," I interjected, ** does not modern physics offer a
certain support to the assumption of a discontinuity ? Does
not the Quantum Theory point to an atomistic structure of
energy, and hence also of events that are to be imagined as
happening in jerks and as involving relations expressible in
whole numbers ? "

Einstein gave an answer of epigrammatic brevity and

DISCONNECTED SUGGESTIONS 209

flavour. " The fact that these phenomena are expressible in
whole numbers must not be construed into an argument
against continuous happening. Just imagine to yourself for
a moment that beer is sold only in whole litres ; would you
then infer that beer, as such, is discontinuous ? "

What achievements are to be expected of astronomy in the
present era ?

This question would have a special meaning if it were
assumed that the astronomer who works in observatories is
surrounded by solved problems, and can no longer hope to
solve problems having the universal significance of those of
Copernicus or Kepler. This assumption, however, would not
be in agreement with the actual state of affairs.

Einstein indicated to me a number of fundamental prob-
lems that present themselves to modern astronomy, and the
solution of which he expected of future times.

Above all, the geometrical and physical constitution of the
stellar systems will, in the main, become revealed.

At present we do not yet know whether Newton's Law of
Attraction holds, at least approximately, for configurations of
the type of the Milky Way and of the spherical clusters of
stars — ^that is, in extents of space in which the influence of
space-curvature would become appreciable. The rapid pro-
gress of recent astronomy justifies our great hopes that the
solution of this universal problem will be found within the
coming decades.

In distant connexion with this we also touched on the
question of the habitability of other worlds. This theme of
Fontenelle, " la plurality des mondes habits," which has
again become a centre of public interest, owing to investigations
of Mars, has evoked a storm of discussion. We hear the noisy
war-cries of geocentric scientists who wish to regain for the
earth her shattered supremacy in astronomy, and who claim
the existence of organic forms as the sole prerogative of our
planet. It is scarcely necessary to mention that Einstein
rejects the motives of these human and all-too-human in-
dividuals as small-minded and short-sighted. Creatures in
distant worlds are derived from, and are subject to, conditions
of organic nature, of which we can form no idea by deductions
14

210 EINSTEIN THE SEARCHER

from the world which we inhabit. But to deny their existence
on numberless constellations, or to demand an ocular proof
of their presence, is no better than to assume the point of view
of an infusoria to whom there is no life other than that in a
dirty drop of ditch-water.

The idea of the atom as the ultimate structural element
involves a philological as well as a conceptual contradiction.
For atomcs signifies the indivisible, the no-further-divisible,
whereas the idea of a body, however small, an element of
structure differing from zero, demands, at least geometrically,
further divisibility. Even the original founders of the theory
of atoms, Leukippus, Epicurus, and Democritus, assigned
definite forms to the ultimate components, and we may read
in the splendid work of Lucretius how he infers from the
nature of substance that the ultimate particles are smooth,
round, or rough, or have the shapes of hooks and eyes. The
further analysis pressed forward, the more the simplicity of the
original idea vanished. Microcosms came to be regarded as
copies of macrocosms, and the atoms of present-day science
actually exact from us that we should regard them as worlds
in themselves.

Einstein acceded to my request that he might give a sketch
of the latest achievements of science sufficient to provide an
approximate idea of the atomic model. According to the
researches of Rutherford and Niels Bohr, we are to picture it
as a planetary system.

The central body of this system is represented by a positively
charged nucleus, which constitutes almost the whole mass of
the atom, surrounded by a certain number of electrons, negative
charges, that move in uniform circular or elliptic orbits about
the nucleus. There is thus a certain analogy that allows us
to regard the nucleus as the sun, and the electrons as the
planets of this S3^tem.

The number of these electrons varies between the limits
I and 92, according to the chemical constitution of the element.
The smallest number occurs in the case of heUum (in which
there are two), and of the hydrogen atom, in which only one
electron-planet describes its circular path about the nucleus.
In other atoms there are probably more compHcated orbits,

DISCONNECTED SUGGESTIONS 211

although they are more or less approximately circular. Ac-
cording to this still very new theory, which is supported by
very convincing facts, the electrons are to be imagined as
arranged in concentric shells (like the layers of an onion),
among which the innermost shell plays a distinctive part
inasmuch as the number of the electrons arranged in it decides
the chemical character of the atom in question. It sometimes
occurs that electrons spring, under external influence, from one
orbit to another ; when the electron jumps back to the original
orbit, light is emitted. An essential fact is to be noted :
Whereas any arbitrary orbits of any arbitrary radius may
occur in a planetary system of the celestial regions, the mani-
fold of these orbits in the case of the electrons is restricted,
in that only certain orbits are possible, namely, those that are
determined mathematically by the quantum condition.

" Perhaps," I interrupted, '* the whole analogy may be
inverted. If the atom is considered analogous to a planetary
system in the model, it should be admissible to regard our
true planetary system as a cosmic atom. And then, long after
we have become accustomed to regard our earth as playing the
part of a grain of sand, the sovereignty of the sun, too, would
be past. The whole majesty of the solar system as far as the
orbit of Neptune would then shrink to a configuration com-
pared with which the world of a grain of sand would be
infinitely complex."

" This fantastic inversion is permissible up to a certain
extent," said Einstein, " but we must not lose sight of the
fact that there is a cardinal difference. If we disregard the
enormous disparity in dimensions, the analogy is far from
exact owing to the circumstance that the atom is only an
element of structure, whereas the true planetary system is an
extraordinarily complex structure in itself. Thus the differ-
ence between a simple thing and one that is very highly
complex still remains."

" But, Professor, may not a similar complexity yet be
discovered in the atom ? It may be merely a difference of
philosophical view from the primary idea to that of regarding
the electrons as circulating like planets. May we not con-
jecture that in each successive step we are merely carrying out
a true regressus in infinitum ? "

212 EINSTEIN THE SEARCHER

" That seems highly improbable," he replied, " although,
of course, structural investigations can never cease. At first
they are directed at the more remote object of finding out why
certain atoms are radioactive, that is, exhibit a tendency to
disintegrate. It has already been established that this ten-
dency is a property of the positive nucleus, of which little is as
yet known. This means that the nucleus is not simple, yet
it does not open up the possibility of an unending regression.
Our aim must be to get a clear insight into the constitution
of the nucleus, as regards the positive and negative charges,
and it is my opinion," he concluded, " that beyond this there
will be no further subdivision of matter."

When Goethe writes of the immovable pole in the flux of
phenomena, we recognize that his beautiful remark pronounces
an elegy to the possibility of attaining ultimate simplicity.
Einstein's utterance, if I understand him aright, converts this
elegy into a song of hope. If the subdivision of matter
actually has an end somewhere, then we are now on the
threshold of ultimate things, we are near the immovable pole,
which we are capable of reaching.

" Every new truth of science must be such that, in ordinary
writing, it may be communicated completely within the space
of a quarto leaf." Kirchhoff made this remark, and gave a
suificient, if not literal, demonstration of its truth. When
Bunsen and he published the first notice about spectral
analysis, they compressed their publication into the small
space of three printed pages.

But what is to happen if the new truth should be built
up of very comprehensive materials, when it requires many
Hnks, of which none can be omitted if the truth is to be
made intelligible ? Would Kirchhoff's quarto page still be
sufiicient ?

" Certainly," said Einstein, " provided, of course, that it is
addressed to a reader who has already mastered what went
before — ^that is, to one who is so far acquainted with the older
facts that he has to learn only the really new part of the new
truth."

" That sounds very hopeful," I remarked, *' for then it

DISCONNECTED SUGGESTIONS 213

should also be possible to describe very briefly the theory of
relativity."

** Let us rather say its essentials — the heart of the matter.
Well, then, get your Kirchhoff page ready. We shall see
whether we can set out on it the special theory of relativity."

The totahty of our experience compels us to assume that
light travels with a constant velocity in empty space. Like-
wise, our whole experience in optics compels us to recognize
that all inertial systems are equivalent ; these are systems
that are produced from an allowable one by means of a uniform
translation. An allowable system is one in which Galilei's
and Newton's Law of Inertia holds. (This law states that a
moving body that is left to itself retains its direction and
velocity permanently.)

Now, the law of the constancy of light propagation seems
to conflict with the classical principle of relativity, according
to which the velocity of a ray of light assumes different values
in the moving system according to the direction of the ray.

This apparent incompatibility arises from the following
unproved assumptions :

(a) If two events are simultaneous with regard to one
inertial system, they are also simultaneous with regard to
any other inertial system.

(b) The length of a measuring-rod, the shape and size of a
rigid body, and the rate of a clock are independent of their
motion with respect to the system of reference used, provided
this motion is rectilinear and non-rotational.

These assumptions must be discarded if this disagreement
is to be eliminated. If we substitute for them the assumption
that all inertial systems are equivalent and that the velocity
of light in vacuo is constant, we get :

(i) That the dimensions of bodies and the rate of clocks
have a functional relation to the motion.

(2) That the equations of motion of Newton require to
be modified ; this modification leads to results that, for rapid
motions, differ appreciably from those of Newton.

This is, in a very compressed form, the meaning of the
special theory of relativity.

As there is still some space left on our quarto page, we

214 EINSTEIN THE SEARCHER

may add a remark that, it is hoped, will make a little clearer
the above-mentioned discrepancy.

Let us choose as our system of reference an express train
1 8 miles long. There are two passengers — Mr. Front, right at
the front of the train, and Mr. Back, at the extreme end of the
train, so that a rigid distance of i8 miles separates the two
passengers. The carriages are transparent, so that the two
passengers can signal to one another. They are, moreover,
furnished with ideal clocks that run at exactly the same rate.

First, suppose that the train is at rest . Back is just opposite
milestone loo, whilst Front is opposite milestone ii8. By
means of a flash, Back signals to Front his time, exactly
12 o'clock. It takes Hght very nearly xrr.wfr second to
traverse the length of the train — 18 miles ; hence the flash will
reach Front at 12 o'clock Yiy,iwij second. Exactly the same
result would have come about if Front had signalled his time
to Back. Light makes no difference in travelling forwards
and backwards. If the train moves at a great speed, the two
travellers can conduct the same experiment as when the train
was at rest. They will then set the time that light takes to
travel from Back to Front equal to the time that it takes to
traverse the same way in the reverse direction. But this
phenomenon will assume a different aspect if viewed from the
railway embankment. An observer on the latter would
affirm that light does not take the same time in travelling the
length of the train in one direction as it does when travelling
in the opposite direction.

For the ray of light moving in the forward direction has
to traverse not only the distance between Back and Front,
but also the very short distance that Front has moved forward
during the interval that the light has been moving ; whereas,
inversely, the flash sent out by Front to Back will traverse
a distance that is correspondingly less than that between the
passengers, since Back is moving towards the signal.

Thus the duration of the two phenomena of light propaga-
tion is the same or different, respectively, according as it is
judged from the train or from the embankment. In other
words, the judgment of the length of time depends on the state of
motion of the observer.

All further pronouncements of the special theory of rela-

DISCONNECTED SUGGESTIONS 2115

tivity are based on the preceding arguments of the relativity
of time.

Would Man be able to construct a Science if he possessed
one sense less than at present — ^for example, if he were deprived
of sight ? Let us apply this to a definite case. In the new
physics the velocity of light plays a decisive part as a world-
constant. At first sight it would appear impossible for us
to determine it and recognize its importance, if we had not at
our disposal some organ which enabled us to become aware of
optical phenomena.

But, as Einstein explained to me, even under such difficult
circumstances, it would be possible to build up a science, for
the reason that phenomena, as far as they are perceptible,
may be transformed so that they become manifest to other
senses if one sense should be absent. For example, the
electrical conductivity of selenium is strongly influenced by the
amount of illumination that falls on it. Thus light acts on a
selenium cell, causing changes of current intensity, which in
their turn may be perceived by feeling, or by chemical action
on the mucous fluid of the tongue. Ultimately we are con-
cerned only with a differentiation that enables us to refer
identical experiences to identical events. We should certainly
encounter enormous difficulties in endeavouring to form a
physical picture of our surrounding world if the number of our
senses should become less than the organs with which we actu-
ally operate. Yet, in principle, we should be able to overcome
all difficulties by means of much lengthened and complicated
lines of research, even if we should have only a single sense
left, or if we had only one at the very outset . The construction
of a Science would then be possible, and would give the same
results, although it might be propounded only after a delay of
perhaps millions of years.

[It is naturally assumed that the intellect is retained, as
this is the necessary condition for all scientific research. Since
the degree of understanding depends on the senses — nihil est
in intellectu, quod non priusfuerit in sensu — we may conjecture
that a human being with only one sense organ would work
with a minimum degree of understanding, which would be
insufficient for the acquirement of any knowledge whatsoever.

216 EINSTEIN THE SEARCHER

This transcendental question, which lies almost beyond the
bounds of discussion, was not touched on in our conversation,
as the subject was restricted so that it should not drift into
metaphysical regions.

Nevertheless, I should like to mention that a speculation
of this kind is recorded in the history of science. Condillac,
in a study teeming with ideas, investigates the behaviour of
a " Statue," that he represents as a human being, with the
assumption that there is at first no idea in the soul of this
statue-person. This living creature is enclosed in a marble
envelope, the sole exterior organ of which is at first the organ
of smell. He then shows that by means of this single sense
all manner of sensations and expressions of will may develop
in his " statue." Condillac does not, however, undertake to
give a convincing proof that this creature, restricted to the
organ of smell, would be able to discover physically the relation-
ships that hold in physical nature, and thus to build up a
scientific system. Thus Einstein, in his discussion, goes
considerably further than the author of this statue.]

Has the " eternal repetition," as outlined by Nietzsche,
any meaning ?

The sage of Sils-Maria tells us that this revelation came
to him midway between tears and ecstasy, as a fantasy
with a real meaning. The crux of his idea is a finite world
built up of a finite number of atoms. From the fact that the
present state emerges out of the immediately preceding one,
the latter from the one just before, and so on, he concludes
that the present state exhibits repetition both forwards and
backwards. All becoming recurs and moves in a multiple
cycle of absolutely identical states.

Let us discard for the moment all philosophical objections,
above all this, that the recurrence of the same disposition
of atoms may not necessarily entail the recurrence of the
same psychical states. Furthermore, let us suppress the
cynical thought that in the return to the same state the world
would have reason to enjoy extreme happiness only for
moments, but to lament for aeons. Then we are left with the
comparatively simple question : Is this repetition, from the
point of view of physics, conceivable and possible ?

DISCONNECTED SUGGESTIONS 217

It would be the death-knell of Nietzsche's idea if the answer
of a great physical research scientist were entirely in the
negative. But Einstein still allows it a small measure of life.
" Eternal repetition," so he expressed himself, " cannot be
denied by science with absolute certainty." The disciples of
Nietzsche will have to rest satisfied with this very small con-
cession. For what, in Nietzsche's eyes, is a logical necessity
becomes transformed by Einstein's supplementary remark
into a vague assumption, the product of fantasy. From
the point of view of physics the recurrence of the same con-
dition is to be regarded as '* enormously improbable." This
statement is founded chiefly on the famous second Law of
Thermodynamics, according to which the processes of Nature
are in the main irreversible, so that a one-sided tendency is
expressed in natural phenomena. The fact that the course
of phenomena is in only one sense or direction speaks in
favour of the view that the events of the world are to be re-
garded as occurring only once.

So that when Nietzsche, in contradistinction to this,
vigorously supported the doctrine of repetition, he contra-
dicted at least one important recognized theorem of physics.
The fact that he did not become conscious of this contradiction,
but that, on the contrary, he regarded his idea as the most
important event in the development of his intellect, may be
regarded as an example of a docta ignorantia. But it is
allowable, too, that philosophic fantasies that complete the
poetical picture of the universe should be given expression.
And Nietzsche would presumably have been deprived of a
degree of pleasure if he had been aware of this second law.

" Truth is the most expedient error " ; this statement may
be traced back to a sequence of thought developed by Nietzsche.
But the Eternal Repetition is shattered by just this remark,
for judged by its consequences it would be a very inexpedient
error.

Supposing we should succeed in exchanging thoughts with
the inhabitants of distant worlds and should, through them,
acquire the elements of a civiUzation superior to our own,
would this knowledge prove a blessing to us or the reverse ?

The word " superior " must, of course, be treated circum-

218 EINSTEIN THE SEARCHER

spectly. It is to denote only that, relatively, this distant
civilization bears somewhat the same relation to our civiliza-
tion of to-day as our own bears to that of an Australasian
negro or an anthropoid ape. There are fanatics of progress
whose wishes plunge headlong and without restraint into the
future, and to whom nothing could be more desirable than the
sudden appearance of a civilization that, as they opine, would
at one stroke carry us " forward " many thousands of years.

But ^;he view of these magicians with their seven-league
boots is untenable. Let me cite a mere outHne of the many
opposing arguments in a few words of Einstein. " Every
sudden change in the conditions of existence, even if it occurred
in the form of a higher development, would come upon us
like a doom, and would probably annihilate us, just as the
Indians succumb to the civihzation that has outstripped
them. The tragedy of our own highly civilized times is that
we cannot create the social organizations that have become
necessary as a consequence of the technical advances of the
last century. This has given rise to the crises, impasses, and
senseless competition between nations, and to the impoverish-
ment of defenceless individuals. These deplorable conditions
would become inconceivably accentuated if we were to be
invaded by extra-mundane technical sciences of a higher
order."

Nevertheless, there is still a possibility that the " superior
civilization " might contain indications of the organizations
which we lack. Instead of entering on the question of this
Utopia, we confined ourselves to comparing past conditions
in our world with present ones. Did we not have the most
promising preliminaries for an organization that was devoid of
friction and tended to reduce the competition between nations
in the numerous international institutions that drew together
a great section of the intellectual world to work in co-operation ?
Are there hopes that this international coalition will be
resumed ?

Einstein expressed himself optimistically, not to do homage
to an organization artificially formed, but to extol the world-
wide mastery of intellect. " Even if international congresses
were to be swept away," he said, " international co-operation

DISCONNECTED SUGGESTIONS 219

would not be abolished, as it effects itself automatically." I
should venture to assert that if all these congresses were to
cease, we should not even have cause to fear that there would
be an appreciable diminution in the combined effort of research.
If certain developments are hindered by political conditions,
it is only due to the resulting economic hardships affecting
individuals in their work and robbing them of their intellectual
freedom. The real friends of Truth have always clung to-
gether, and do so actually now ; indeed, many feel the tie to
be closer than that connecting them to their own country.
In spite of all obstacles and boundaries they will never cease
to find contact with one another !

CHAPTER XI
EINSTEIN'S LIFE AND PERSONALITY

WE know from the biographies of great thinkers that
they seldom personify the character of a dramatic
ideal. They are not heroes of fiction who pass
through complex experiences and struggle with mysterious
problems of existence that may unduly excite the imagina-
tion of observers. Whoever follows their development re-
marks in the majority of cases the predominance of the inner
life, the course of which is discoverable only by study of their
works, no clue being given in the confusion of ordinary exterior
manifestations. An eminent man of thought, whose energies
are concentrated on mental effort, rarely finds time to present
in addition an interesting figure in the epic sense. The poet
who moulds his forms from life finds little scope in him as a
model, and only in exceptional cases has he succeeded in
idealizing the savant in a work of art.

It would be a fruitless undertaking to treat Einstein's life
as one of these exceptional cases. It is possible to trace the
various phases of his development, yet neither the writer nor
the reader must disguise from himself the fact that such
outlines give only the external picture of the man and chrono-
logical events of importance. Nevertheless, a book of which
he forms the theme cannot pass over the task of giving his
curriculum vitce. And if it should partly appear aphoristic
and disjointed, it must be borne in mind that this account
originated from conversations and scraps of conversation
that touched on various episodes of his hfe, according as they
had a bearing on the subject under discussion.

The story of Einstein's Hfe begins at Ulm, the town which
possesses the highest building in Germany. Gladly would I
stand on the belfry of the Ulm Cathedral in order to obtain a

220

EINSTEIN'S LIFE AND PERSONALITY 221

general survey of Einstein's youth. But the view discloses
nothing beyond the bare fact that he was born there in March
1879. The detail which has already been mentioned above,
namely, that it was something physical that first arrested the
child's attention, remains to be noted. His father once showed
the infant, as he lay in his cot, a compass, simply with the idea
of amusing him — and in the five-year-old boy the swinging
metal needle awakened for the first time the greatest wonder-
ment about unknown cohesive forces, a wonderment that was
an index of the research spirit that was still lying dormant in
his consciousness. The remembrance of this psychical event
has a significant meaning for the Einstein of to-day. In him
all the impressions of early childhood seem to be still vivid, the
more so as all other physical occurrences, such as the falUng
of an unsupported body, left no impression on him. His
attention was fixed on the compass, and the compass alone.
This instrument addressed him in oracular language, indicating
to him an electromagnetic field that was in later years to
serve him as a domain for fruitful research.

His father, who had a sunny, optimistic temperament, and
was inclined towards a somewhat aimless existence, at this
time moved the seat of the family from Ulm to Munich. They
here Hved in a modest house in an idyllic situation and sur-
rounded by a garden. The pure joy of Nature entered into
the heart of the boy, a feeUng that is usually foreign to the
youthful inhabitants of cities of dead stone. Nature whis-
pered song to him, and at the coming of the spring-tide infused
his being with joy, to which he resigned himself in happy
contemplation. A religious undercurrent of feeHng made
itself manifest in him, and it was strengthened by the ele-
mentary stimulus of the scented air, of buds and bushes, to
which was added the educational influence of home and
school. This was not because ritualistic habits reigned in the
family. But it had so happened that he learned simultaneously
the teaching of the Jewish as well as the Catholic Church ;
and he had extracted from them that which was common
and conducive to a strengthening of faith, and not what
conflicted.

Youthful impetuosity, which in boys of a similar age
usually expresses itself in rash enterprises and loose tricks, did

222 EINSTEIN THE SEARCHER

not appear in him. His spirit was adjusted to contemplation,
and an inborn fatalism, diffused with a super-sensuous element
appertaining to dreams, restrained him from responding to
external impulses. He reacted slowly and hesitatingly, and
he interpreted what his senses offered him and all the Httle
experiences of early days in terms of a reverence reflected from
within. Words did not easily rise from his lips, and measured
by the ordinary scale of rapidity of learning and readiness in
answering questions, he would scarcely have been judged to
possess unusual gifts. As an infant he had started to talk
so late that his parents had been in some alarm about the
possibility of an abnormality in their child. At the age of
eight or nine years he presented the picture of a shy, hesitating,
unsociable boy, who passed on his way alone, dreaming to
himself, and going to and from school without feeling the need
of a comrade. He was nicknamed " Biedermaier," because he
was looked on as having a pathological love for truth and
justice. What at that time seemed to be pathological, to-day
appears as a deeply rooted and irrepressible natural instinct.
Whoever has got to know Einstein as a man and as a scientist
knows that this failing of his boyhood was but the forerunner
of a very healthy outlook.

Signs of his love for music showed themselves very early.
He thought out little songs in praise of God, and used to sing
them to himself in the pious seclusion that he preserved even
with respect to his parents. Music, Nature, and God became
intermingled in him in a complex of feeling, a moral unity,
the traces of which never vanished, although later the religious
factor became extended to a general ethical outlook on the
world. At first he clung to a faith free from all doubt, as had
been infused into him by the private Jewish instruction at
home and the Catholic instruction at school. He read his
Bible without feeling the need of examining it critically ; he
accepted it as a simple moral teaching and found himself little
inclined to confirm it by rational arguments inasmuch as his
reading extended very Httle beyond its circle.

Painful inner conflicts were not wanting. Jewish children
formed a small minority in the school, and it was here that the
boy Albert felt the first ripples of the anti-semitic wave that,
sweeping on from without, was threatening to overwhelm

EINSTEIN'S LIFE AND PERSONALITY 223

master and pupil alike. For the first time he felt himself
oppressed by something that was not in harmony with his simple
temperament. His modesty made him a prey to injustice,
and in defending himself his originally gentle and restrained
nature gained a certain independence and individuality.

If one may speak of achievements at all in a preparatory
school, those of Albert were of the average modest level. He
was careful as a pupil, generally satisfied requirements, but in
no way betrayed special talents : indeed, so much the less, as
he showed himself to be possessed of a very uncertain memory
for words. The methodic plan of the elementary school that
he attended to his tenth year was, however, not other than
the usual scheme mapped out by drill-masters ; it made up
for what was lacking in an understanding of the pupils by
applying drastic strictness. The beautiful sentence of Jean
Paul : " Memory is the only paradise from which we cannot
be banished," finds no echo in Einstein's school memories,
of which he has often spoken to me without a shadow of regret
for a lost paradise. He told me with bitter sarcasm that his
teachers had the character of sergeants — ^those later in the
gymnasium (secondary school) were of the nature of lieutenants.
Both terms are used in the pre-armistice sense, and his words
were directed against the self-opinionated tone and customs
of these garrison-schools of earlier days.

The next stage of his development was a course of study
at the Luitpold-Gymnasium in Munich, which placed him in
the second class. In Einstein's retrospect of these days more
friendly recollections present themselves, connected, however,
only with particular persons, and not breathing praise in
general ; on the contrary, from his account, it is clear that
although he conceived affection for individual teachers, he
felt the tone of the institute as a whole to be rough. As we
know, many things have been changed in these schools since
then, following on a revulsion from the convict atmosphere
that used to characterize them, and which meant suffering
enough for the pupils. The result was that the schoolboy
Einstein developed a contempt for human institutions and
assigned Httle value to the subjects of study which he w£ls
obUged to absorb in schematic form without the application of
his own mental energy. This gloomy picture is relieved at

224 EINSTEIN THE SEARCHER

points by the presence of several teachers, above all, one called
Ruess, who took pains in exposing the beauty of classical
antiquity to the fourteen-year-old boy. We learn elsewhere
that Einstein at present admits the humanistic ideal for the
school of the future only under very restricted limitations.
But when he thinks of this teacher and his influence, a warm
appreciation of classical study vibrates in his words, occasion-
ally rising, indeed, to an unbounded enthusiasm for the treasures
of Greek history and Hterature. His instruction was not
restricted to the acquisition of a perspective of the antique.
Under the direction of the same teacher, he was introduced
into the poetic world of his native country, and learned the
magic of Goethe in his " Hermann and Dorothea " ; this poem,
as he confesses, was explained to him in a really model manner.
Thus there were some oases in the desert of schematic teaching :
they served as refreshing halts for the spirit of the eager young
searcher after knowledge.

We must go back one or two years to note a weighty ex-
perience, which occurred when he made his first acquaintance
with elementary mathematics ; this subject presented itself
to him with the intensity of a revelation. It did not happen in
the ordinary course of school- work, but was due to a sort of
wizard-Hke inquiring inner spirit that plied him with questions
and that gave him inward thrills of joy when he found a sharp-
witted solution. From the very beginning Albert proved
himself to be a good solver of problems, even before he achieved
an arithmetical virtuosity, and before he knew the technique
of equations. He helped himself by means of little tricks,
experimented roundabout inventions, and was happily excited
when they led to the goal. One day he asked his uncle, Jacob
Einstein, an engineer who lived in Munich, a certain question. He
had heard the word " algebra " andsurmisedthat his uncle would
be able to explain the term to him. Uncle Jacob answered :
*' Algebra is the calculus of indolence. If you do not know a
certain quantity, you call it x and treat it as if you do know it,
then you put down the relationship given, and determine this
X later." That was quite sufficient. The boy received a book
containing algebraic problems that he solved all alone in accord-
ance with this not exhaustive but expedient direction. On
another occasion Uncle Jacob told him the enunciation of

EINSTEIN'S LIFE AND PERSONALITY 225

P3^hagoras' theorem without giving him a proof. His nephew
understood the relationship involved, and felt that it had to
be founded on some reasoning. Again he set about all alone
to furnish what was wanting. This was, however, not a case for
the " calculus of indolence " with an x that was to be deter-
mined. Here it was a question of developing a facility for
geometric argument, such as very few possess at such an early
stage of development. The boy plunged himself for three
weeks into the task of solving the theorem, using all his power
of thought. He came to consider similarity of triangles (by
dropping a perpendicular from one vertex of the right-angled
triangle on to the hypotenuse), and was thus led to a proof
for which he had so ardently longed ! And although it con-
cerned only a very old well-known theorem, he experienced
the first joy of the discoverer. The proof that he had found
proved that the ingenuity of the worrying young mind was
awakening.

A new world was opened for him when he made the acquaint-
ance of A. Bernstein's comprehensive popular books on scientific
subjects. This work is looked on nowadays as being some-
what antiquated and, in the eyes of many a professional
scientist, has sunk to the level of a pseudo-scientific " shocker " ;
even when Einstein as a boy made explorations in it, there were
signs of rust and decay in the work, for it originated in the
fifties of the previous century and, in point of subject-matter,
had long been transcended. Yet it could be read then — and
even now — as a story containing thousands of interspersed
physical, astronomical, and chemical wonders, and for the boy
Einstein it came to be a true book of Nature, which presented
to his mind, greedy for knowledge, as much as it did to his
imagination.

Other vistas were opened up to him by Biichner's Kraft
und Stoff (Force and Substance), a book the cheapness of which
he could not yet discern, but which called up wonder in him
without rousing his criticism. In addition, his attention was
chiefly occupied by a handbook of elementary planimetry,
containing an abundance of geometrical exercises, which he
fearlessly attacked and within a very short time solved almost
in their entirety. His dehght grew when he ventured into
the difficulties of analytical geometry and infinitesimal calculus
15

226 EINSTEIN THE SEARCHER

quite apart from the curriculum oi his school-work. Liibsen's
textbook had fallen into his hands, and these directions
sufficed for his audacious spirit. Whereas many of his school
companions were still standing undecidedly before the pools
of theorems of congruence and repeating decimals, he was
already disporting himself freely in the ocean of infinitesimals.
His work did not remain concealed, and gained appreciation.
His mathematical teacher declared that the fifteen-year-old
boy was ripe for university study.

Yet he was not to find a way into the open by matriculating
very early, but through an event that unexpectedly threw
him into new surroundings of life. In 1894 his parents trans-
ferred their abode to Italy. The chronicler has nothing to
report of pangs of separation in Albert when he left Bavarian
soil. He was glad to get away from the drill academy, Luitpold,
and, as an inhabitant of Milan, he enjoyed the change in his
existence, and was not encumbered by attacks of home-sick-
ness. All in all, he had felt himself in an unhappy position
under school compulsion in Munich, in spite of the mathe-
matical deHghts he had provided for himself, and in spite of the
rapturous moments that musical revelations had created for
him since his twelfth year. Defiance and distrust against out-
side influences had remained active in him as forces that did not
allow the happy disposition proper to his age to assert itself.
But now the fetters had fallen and the pent-up joy of Ufe
burst forth as if through opened sluices. The sun and land-
scape of the South, ItaUan manners of life, art freely displayed
in the market-place and on the street, realized for him dream-
pictures that had appeared to him earlier during the hours
of oppression. Whatever he saw, felt, and experienced lay
outside the ordinary course of his Hfe, awakened his sense for
natural and human things, and set his spirit free from all bonds.
There was no question of his going to school in the first six
months. He enjoyed complete freedom, occupied himself
with literature, and undertook extended excursions. Starting
from Pa via, he wandered all alone over the Apennine to Genoa.
Whilst he was being intoxicated with the sublime Alpine
landscape, he came into contact with the lower stratum of
the people, who aroused his deepest sympathy. The tour
took him over a short stretch of the Italian Riviera, the

EINSTEIN'S LIFE AND PERSONALITY 227

beauties of which, as depicted by Bocklin, do not seem to
have revealed themselves to him. At that time he was
probably subject to a feeling of upward striving such as
possessed Zarathustra.

With all their joys and inspirations the experiences in Italy
remained but a short episode. Einstein resolved on a new
tour, which was not without a professional purpose. He made
a pilgrimage to Switzerland with the intention of studying
mathematics and physics at the Zurich Polytechnical Institute.
But he was not to be successful in his first effort to gain entrance.
The conditions of entry required a standard in descriptive
sciences and modern languages that he had not yet reached.
So he turned to Aarau, where he was allowed to extend his
knowledge with the help of excellent methods at the Canton
school. Even at the present day Einstein talks with extreme
enthusiasm of the organization of this model school that corre-
sponds in rank approximately to a German Realgymnasium
(or an English Grammar School). There was nothing to
remind him of the continual manipulation of the sceptre of
authority at the Luitpold school barracks ; he easily obtained
his leaving certificate, and now the portals of the Ziirich
Pol5^echnicum were open for him.

He himself was probably not aware that he carried a
marshal's baton in his own mathematical equipment. But,
in looking back, we come across astounding things. For it
is a fact that even in the pupil at Aarau problems had taken
root that already lay in the vanguard of research at that
time. He was not yet a finder, but what he sought as a
sixteen-year-old boy was already stretching into the realms
of his later discoveries. We have here simply to register
facts, and to abstain from making an analysis of his develop-
ment, for how are we to trace out the intermediate steps, and
to discover the sudden phases of thought that lead a very
young Canton pupil to feel his way into a still undiscovered
branch of physics ? The problem that occupied him was
the optics of moving bodies, or, more exactly, the emission
of light from bodies that move relatively to the ether. This
contains the first flash of the grandiose complex of ideas that
was later to lead to a revision of our picture of the world.
And if a biographer should state that the first beginnings of

228 EINSTEIN THE SEARCHER

the doctrine of relativity occurred at that time, he would not
be making an objectively false statement.

The ambitions of the youth by no means reached these
flights of imagination, for whereas the latter signified the coming
power of his wings, he himself set a modest goal. He wished
to become a schoolmaster, and imagined that in choosing this
career he was allowing his hopes to run high. This was in
conformity with the esteem in which he held the status of
teachers. In the Ziirich Technical School there is a section
equipped as a department for preparing teachers, and in this
Einstein studied from the age of seventeen to the age of
twenty-one, perfectly satisfied with the thought of sitting, not
on the pupil's bench, but at the master's desk, and of exercising
a beneficial if limited influence as a preceptor of the young.

He was still under the sway of the feeling that he was
not sufficiently experienced in fife and that he dare not
venture out into the fight for existence in the great turmoil
of the world. He saw in this struggle, which pitted man
against man, led to exhibitions of violence, and aroused
ambition for glittering unrealities, cause only for disgust
and alienation. The prospect of personal success did not
lure him to try force against force. Thus, for the time being,
it was his ideal to lead a very modest existence. From various
quarters he had been given hopes of a position as assistant to
some professor of physics or mathematics. But for unknown
reasons he was everywhere refused. These apparently obscure
grounds, it must be said with regret, become clearer when we
bear in mind his confession of faith. Nor did his hopes of
teaching at a gymnasium seem near fulfilment, as certain
conditions of birth raised obstacles. In the first place, he was
not a Swiss ; in fact, since his stay in Milan he was without a
nationality at all in the bureaucratic sense, and then he had
no personal connexions, without which, at least at that time,
there was no chance of progress even for a talented person.
Yet the young student who was entirely without protection
of any sort had to overcome the cares and satisfy the needs of
daily life. He could not rely on material help from his parents,
who themselves lived in restricted circumstances, and thus
we find him a little later in Schaffhausen and Bern, where he
earned a small pittance as a private tutor.

EINSTEIN'S LIFE AND PERSONALITY 229

He found consolation in the fact that he preserved a
certain independence, which meant the more to him as his
instinct for freedom led him to discover the essential things
in himself. Thus, earlier, too, during his studies at Ziirich
he had carried on his work in theoretical physics at home,
almost entirely apart from the lectures at the Polytechnic,
plunging himself into the writings of Kirchhoff, Helmholtz,
Hertz, Boltzmann, and Drude. Disregarding chronological
order, we must here mention that he found a partner in these
studies who was working in a similar direction, a Southern
Slavonic student, whom he married in the year 1903. This
union was dissolved after a number of years. Later he found
the ideal of domestic happiness at the side of a woman w^hose
grace is matched by her intelligence. Else Einstein, his cousin,
whom he married in Berlin.

In 1901, after living in Switzerland for five years, he
acquired the citizenship of Ziirich, and this at last gave him
the opportunity of rising above material cares. His Uni-
versity friend, Marcel Grossmann, lent him a helping hand by
recommending him to the Svvdss Patent Office, the director of
which was his personal friend. Einstein occupied himself here
from 1902 to 1905 as a technical expert, that is, as an examiner
of appHcations for patents, and this position gave him the
chance of moving about in absolute freedom in the realms of
technical science. Whoever has a strong predilection for
discovery will perhaps feel estranged to find Einstein so long
in the sphere of " invention," but, as Einstein himself em-
phasizes very strongly, both regions make great demands on
clearly defined and accurate thought. He recognizes a definite
relationship between the knowledge that he gained at the
Patent Office and the theoretical results that appeared at the
same time as products of intensive thought.

In 1905, in the midst of his work, the storm broke loose in
him with the suddenness of a hurricane. In quick succession
his mind disburdened itself of the abundance of ideas that
had stored themselves up in the work of the preceding years,
and these ideas signify more to us than a definite stage in the
development of an individual. What physicists have come
to regard as an elaboration of the heritage of GaHlei and
Newton had matured in him. We merely record the title

230 EINSTEIN THE SEARCHER

of dissertations, which appeared in 1905 in the Annalen der
Physik : " Concerning a Heuristic Standpoint towards the Pro-
duction and Transformation of Light " — " Concerning the
Inertia of Energy " — " The Law of Brownian Movement/'
— Then the most important contribution : " The Electro-
dynamics of Moving Bodies," that contained the revolutionary
ideas underlying the special theory of relativity. To these is to
be added a dissertation for his doctorate in the same year :
" A New Determination of Molecular Dimensions."

In all, these represent a Hfe-work that belongs to the
history of science. It was certainly some considerable time
before his work began its triumphal march in the sight of the
world, and it may be added that treasures were hidden in these
disquisitions that were not understood till long years after-
wards. Yet the youthful discoverer was not passed over
without signs of friendly appreciation. He received a letter,
couched in very warm terms, from the celebrated physicist.
Max Planck, who was a complete stranger to him at that
time ; it spoke in glowing words of his essay, *' The Electro-
dynamics of Moving Bodies." This letter was the first
diploma, the forerunner of all the honours that later swept over
him like a tidal wave.

It was his intention to obtain a tutorial position at the Uni-
versity. An appointment to Bern was at first again hindered
by certain obstacles which he would probably have overcome
if he had applied himself energetically to attaining his goal.
He finally received his appointment, but exercised his duties
for only a very short time, as Ziirich now opened her arms to
him. In 1909 he accepted the position of Professor extra-
ordinarius there for theoretical physics, and soon assembled
a grateful audience about himself. Nevertheless, during the
earlier stages of his professorship he found it difficult to sup-
press a longing for the quiet, unexcited Ufe of his patent-ofhce
work, in which he seemed to have had a still greater degree
of ^independence. In 191 1 he accepted a new appointment
as Professor ordinarius to Prague, which offered him more
favourable emoluments as an inducement. In the autumn of
1912 he returned to Ziirich as a Professor at the Polytechnic,
and in the early part of 1914 he was drawn into the strong
magnetic field of the northern capital ; he arrived at the Spree,

EINSTEIN'S LIFE AND PERSONALITY 231

and has, since then, lived among us. He is now a Swiss by
nationality, a world citizen by conviction, and, professionally,
a member of the Berhn Academy and attached in a lecturing
capacity to the University. Here he perfected his works on
relativity, ending in the superlative elaboration of the theory
of gravitation, the beginnings of which stretch back to the
year 1907. He had spent eight years in a concentrated effort
of severe thought to bring it to completion, and perhaps
centuries will be necessary before the world will gain a com-
plete perspective of all the consequences of his theory.

For the theory asks us to brush aside habits of thought
that have claimed an hereditary position in pre-eminent minds.
One of the foremost physicists, Henri Poincar6, had confessed
as late as 1910 that it caused him the greatest effort to find
his way into Einstein's new mechanics. Another whole year
passed before he gave up his last doubts. Then he passed
with flying colours into Einstein's camp, and recommended
Einstein's appointment to the Professorship at Ziirich, in con-
junction with the discoverer of radium, Madame Curie, in an
exuberant letter which may add its note of appreciation here :

" Herr Einstein," so wrote the great Poincar^, ** is one of
the most original minds that I have ever met. In spite of his
youth he already occupies a very honourable position among
the foremost savants of his time. What we marvel at in him,
above all, is the ease with which he adjusts himself to new
conceptions and draws all possible deductions from them. He
does not cling tightly to classical principles, but sees all con-
ceivable possibilities when he is confronted with a physical
problem. In his mind this becomes transformed into an
anticipation of new phenomena that may some day be verified
in actual experience. . . . The future will give more and more
proofs of the merits of Herr Einstein, and the University that
succeeds in attaching him to itself may be certain that it will
derive honour from its connexion with the young master."

We may be tempted to look back and ask whether the
criteria that Wilhelm Ostwald once set up as a test of great
men are verified in Einstein's case. He has certainly not
broken the first and most general rule, the principle of " early
maturity." This showed itself clearly when his impulse to-
wards mathematical knowledge and discovery asserted itself.

232 EINSTEIN THE SEARCHER

and when he penetrated far into the future with his optical
problems. The history of science and of art may offer more
striking examples in this connexion, but at any rate in
Einstein's case the indications are sufficient to serve as a con-
firmation of the rule. On the other hand, the second test of
Ostwald seems to be valid only conditionally when apphed to
Einstein. For Ostwald takes up arms against a " gradual
intensification " of ability, and proclaims it as an almost
universal rule that the exceptional achievement is the privilege
of quite young persons : " what he achieves later is seldom
as impressive as his first brilUant achievement." Thus, in
Einstein's case, the exception is evident. For if we fix on
only two chief discoveries, passing over many others, there is
no doubt that the second (the theory of gravitation) surpasses
the first (special relativity) in both range and significance.
Indeed, we cannot escape from the idea of a " gradual in-
tensification," for the second discovery could come about only
as a result of the first. Moreover, it is not yet night, and there
is nothing to refute the assumption that there will be a further
progression.

Furthermore, Ostwald takes into consideration the tempo
of the intellectual pulse of inspiration to divide the main
types of great men into a classical and a romantic category :
this classification cannot, however, be applied to Einstein.
He is decidedly classical, in so far as his work seems calculated
to serve later generations as a classical foundation for all
mechanical investigations of the macrocosm of the heavens
and the microcosm of atoms. On the other hand, his ver-
satiHty, the mobility and resource of his highly imaginative
mind, stamp him as a romantic spirit. His delight in teaching
would also assign him to this category, for in the case of many
classical spirits there is a decided aversion to imparting in-
struction. So that, although we might well be able to speak
of a synthesis of these two forms, it seems better to estimate
Einstein, not in the light of a ready scheme, but rather as a
type of which he is the unique representative.

Just as the external contour of his life is on the whole
regular and unbroken, so also his inner life is attuned to
simplicity. Nowhere, it might almost be said, do we observe a

EINSTEIN'S LIFE AND PERSONALITY 233

break, a spasmodic turn, or a sudden intensification. Although
he has grasped and suggested so many problems, he himself
presents no psychological riddle, and we meet with no
singularities in analysing his personality. It has already
been remarked several times that Art plays a part in his life.
What I learned from him himself about his affection for music
coincides exactly with what observation clearly discloses.
The expression of his countenance when he is listening to
music is a sufficient indication of the resonances induced in
him. He is confessedly a classicist, and a sincere devotee of
the revelations of Bach, Haydn, and Mozart. What fascinates
and enraptures him above all is that which is directed inwards,
which is contemplative and erected on a religious basis. The
simple masterful flow in musical development and invention
is all-important for him. The architectonic structure that we
marvel at in Bach, the Gothic tendency towards heavenly
heights, perhaps calls up in him sensations that emanate from
his hidden wealth of constructive mathematical ideas. It
seems to me that this possibility is not unworthy of remark.
It suggests a reason for the fact that he gives himself up only
unwillingly to the nervous strain of drama directed at emo-
tional upheaval. He does not gladly overstep the boundary
that separates the simple from the psychologically subtle, and
whenever his desire to understand art requires him to venture
beyond it, his appreciation is not accompanied by genuine
pleasure. His subjectivity does not fix this boundary in
accordance with the ordinary rules of concert aesthetics, which
are actually not rules at all, but only changeable valuations
and crystallizations of the feelings of certain groups of people.
He gives himself up quietly and freely to what is presented,
but makes no special effort to assimilate experiences to which
his being does not spontaneously react. There would be no
meaning in seeking to mark off the limits of his receptivity in
accordance with this, and to tell him that it is too Umited, and
that it should be enlarged, and that he should not regard as an
opinionated exaggeration what appears to others to be a deep
and mighty revelation, or seems to be possessed of divine
sweetness. He would be able to point out that even in the
case of masters of the musical art a change of faith was not
a rare occurrence, and that they learned anew, or rejected what

234 EINSTEIN THE SEARCHER

they once idolized, and very often found no permanent haven
in their own faith. Whoever, Hke Einstein, gives himself up
to the simply contemplative, and feels no impulse towards
sensationalism, is spared the task of learning afresh, and finds
still one world left for him even if many other worlds are in-
accessible. To mention only the main features, then, neither
Beethoven as a composer of symphonies, nor Richard Wagner,
denote the pinnacles of music for him ; he could live without
the Ninth Symphony, but not without Beethoven's ensemble
music. The number of composers and compositions which
are not a necessity of life for him is very considerable. It
includes the majority of romanticists, the erotically inclined
school of Chopin and Schumann, which revels in sensation,
and, as already mentioned, the neo-German dramatic com-
posers. He has much objective admiration for them, yet he
does not conceal the fact that he also feels lively opposition
in the gamut of his sensations. He regards the properly
modern productions as interesting phenomena, and has
various degrees of disapproval for them, extending to complete
aversion. It costs him an effort to hear an opera of Wagner,
and when he has done so, he returns home bearing with him
the leitmotiv of Meister Eckhard : " The lust of creatures is
intermingled with bitterness." In general he seems to take
up approximately the point of view of Rossini. Wagner
gives him wonderful moments, followed, however, by periods
of acute emotional distress. I need hardly add that I myself,
who confess to being an ultra-Wagnerite, never strove in my
conversations with Einstein to make my opinion prevail
against his. For I am deeply convinced that in this matter
there is no question of right and wrong, and that every musical
valuation represents no more than an accidental judgment
dependent on one's own nature, entirely ego-centric and thus
objectively of no account.

Einstein also occupies himself in an active sense with
music, and has developed into a very fair violinist, without
claiming higher degrees of achievement. Among other things
I once heard him play the violin part of a Brahms Sonata,
and his performance approached concert standard. He draws
a beautiful tone, infuses expression into his rendering, and
knows how to overcome the technical difficulties. Among

EINSTEIN'S LIFE AND PERSONALITY 285

the supreme artists of his instrument who have exerted a
personal influence on him, Joachim assumes the first place.
Einstein still speaks with great enthusiasm of Joachim's
performance of Beethoven's Tenth Sonata and of Bach's
Chaconne. He himself plays the latter piece, for which the
purity and accuracy of his double and multiple stopping fits
him. Whoever chooses the right moment — ^this good fortune
has not yet befallen me — may overhear Einstein at his pianistic
studies. As he confessed to me, improvisation on the piano is
a necessity of his life. Every journey that takes him away
from the instrument for some time excites a home-sickness for
his piano, and when he returns he longingly caresses the keys
to ease himself of the burden of the tone experiences that have
mounted up in him, giving them utterance in improvisations.

The regular run of concerts in which displays of bravura
play an important part finds little favour with him ; above all,
he is not a worshipper of the orchestral conductor, whom he
regards only as an interpreter and not as a virtuoso on the
orchestral instrument . He expressed this idea in unmistakable
words : " The conductor should keep himself in the back-
ground." I believe that his dearest wish would be to breathe
in the tones without a personal or material medium, merely out
of the air or out of space. Furthermore, I believe that there
is an unfathomable connexion between his musical instinct
and his nature as a research scientist. For the ear, as we
know from Mach, is the true organ that enables us to experience
space, and thus things may occur within the ear of the investi-
gatorjof space that may have a different significance from
that of music which is represent able in tones. I strongly
doubt whether traces of compositional form occur in Einstein's
tone-monologues, but perhaps they contain examples of an
art for which the aesthetics of a distant future may find a
name.

With regard to higher literature, and indeed all writings
not connected with science, Einstein has little to say. He
himself rarely directs conversation on to this topic, and still
less rarely does he give vent to an enthusiastic outburst that
betrays warm interest. He restricts himself to making short,
aphoristic comments, and now and then allows his listener

236 EINSTEIN THE SEARCHER

to gather that he can easily imagine an existence without
literature. The number of accepted novels, tales, and poetic
works which he has not read is legion, and all the pretentiously
artistic, historical, and critical writings that are added to them
have attracted only a very momentary interest from him.

I have never seen him attracted in any way by the pro-
mising aspect of some new book intended for diversion. If
such a one happens to get into his hands, he merely places it
among the others. At times I was constrained to think of
Caliph Omar's words : " If the book contains what is already in
the Koran, it is unnecessary ; if it contains something else, it is
harmful.'' It is harmful at least in the sense that it robs us
of time that may be better spent in another way. I am
purposely exaggerating here to make it quite clear that Einstein
finds full satisfaction in a narrow circle of Uterature, and that
he experiences no loss if numerous new works pass by and
escape his notice.

Nevertheless, he speal^s with reverence of a series of authors,
to whom he owes enrichment : among them are the classical
writers, who naturally occupy the highest position, with
certain exceptions, which he equally naturally wishes to be
taken as a personal opinion and not in the sense of a critical
valuation. With him the difference reveals itself in the in-
tonation from which we may read a greater or lesser measure
of affection. When he says " Shakespeare," the eternal
greatness seems to ^e inherent in the actual sound of the
name. When he sa^s " Goethe," we notice a slight undertone
of dissonance, which may be interpreted without difficulty.
^ He admires him with the pathos of distance, but no warmth
glows through this pathos.

I had ventured to deduce from my knowledge of his nature
the men and the works which, in my opinion, should awaken
strong echoes in him. A fairly clearly defined line leads to
the true path. Outside of any systematic series, I may
mention Dostojewski, Cervantes, Homer, Strindberg, Gottfried
Keller in the positive sense, Emile Zola and Ibsen in the
negative sense. Taken as a whole, this prognostication does
not disagree seriously with his own statement, excepting
that he lays still greater emphasis on Don Quixote and the
Brothers Karamasoff than I had surmised. He expressed

EINSTEIN'S LIFE AND PERSONALITY 237

himself with reserve about Voltaire. He has no belief in
Voltaire's poetic quaUties, and sees in him only a subtle-
minded and amusing writer. Perhaps if Einstein were to
devote himself a httle more intensively to Voltaire and Zola,
he would assign a higher value to these related spirits. But
there is little hope of this occurring, as the wide range of
Voltaire's works tends to restrain him. Time, which the
physicist Einstein has shown to be relative, has an absolute
value for him when measured in hours, and whoever seeks to
persuade him to read thick volumes is not likely to gain his
goodwill.

Our philosophical Uterature is not received with acclama-
tion by him. If some one wished to undertake the task of
ascertaining Einstein's attitude towards philosophy, he would
be well advised to plunge into Einstein's works rather than to
ask him personally. In them the questioner would find ample
hints, pointing towards a new theory of knowledge, the first
indications of which are already perceptible. A great portion
of philosophic doctrine will yet have to pass through the
Einstein filter to be purified. He himself, it seems to me,
leaves this process of filtering mostly to other thinkers, but we
must not lose sight of the fact that these others derive their
views of space, time, and causality from Einstein's physics.
It is thus immediately evident that he does not find revelations
about ultimate things in already extant literature, for the
simple reason that they are not to be found there. For him
famous works represent, in Kant's language, " Prolegomena
to every future system of metaphysics which can claim to
rank as a science." The accent is to be put on the future
that has not yet become the present. He praises many,
particularly Locke and Hume, but will grant finality to none,
not even to the great Kant, not to mention Hegel, Schelling,
and Fichte, whom he barely mentions in this connexion.
To Schopenhauer and Nietzsche he assigns a high position as
writers, as masters of language and moulders of impressive
thoughts. He values them for their hterary excellence, but
denies them philosophic depth. As far as Nietzsche is con-
cerned, whom, by the way, he regards as too glittering, Einstein
certainly experiences ethical objections against this prophet of
the aristocratic cult whose views are so diametrically opposed

238 EINSTEIN THE SEARCHER

to Einstein's own opinion of the relations between man and
man.

Earlier when we were talking of classical poetry he had
particularly emphasized Sophocles as one who was dear to him.
And this name leads us to the innermost source of Einstein as
a man. " I am not here to hate with you but to love with
you," is the cry of Sophocles* Antigone, and this cry is the key-
note of Einstein's emotional existence. I shall not give way
to the temptation to follow those who in the turmoil of the
present day refer to Einstein as a poHtical figure. That would
lead to a description of policy and party arguments that lie
beyond the scope of this book ; so much the less am I inclined
to do so as Einstein's convictions may be expressed very clearly
without reference to schematic terms of a very elastic nature.
An individuality such as his cannot be compressed into a party
programme . And if anyone should insist on placing him among
the radicals or on assigning him far to the left, I should suggest
that it would be better to choose, instead of the classification
right and left, that of above and below. I look up towards his
idealism, whose altitude may perhaps be reached one day by
the raising of our ethical standards. But not by means of
paragraphs of laws. I have seldom heard him talk of such
schematic recipes, but so much the more have I noted utter-
ances which bore witness to a very intense and ever-present
sympathy with every human creature. His programme, which
is written not in ink but in heart 's-blood, proclaims in the
simplest manner the categorical imperative : Fulfil your duty
to your fellow-being : offer help to every one : ward off every
material oppression. " Well, then, he is a socialist," so the cry
runs. If it is your pleasure to call him so, he will not deny you
it. But to me this term seems to denote too narrow limits for
him. I see no contradiction in applying the term, but there is
no perfect congruence. If one word is necessary, I should be
rather more inclined to say that he is in the widest sense a
democrat of liberal trend.

For him the State is not its own aim, nor does he imagine
himself to be the possessor of a panacea. " The attitude of the
individual to socialism," he said, *' is uncertain owing to the
fact that we can never ascertain clearly how much of the iron
compulsion and bhnd working of our economic system may be

EINSTEIN'S LIFE AND PERSONALITY 289

overcome by appropriate institutions." And I should like to
add that such institutions would scarcely have a permanent
result, but that more may be expected from the ethical example
of those who have the power of renunciation. Whoever
reaUzes the motto of Antigone, " I am here to love with you,"
brings us nearer the goal. All in all, our longing continually
flees from the confusion of political considerations to simple
morality. For Einstein this is the primary element, that
which is directly evident and not open to misrepresentation.
It includes sympathy, and, what is more important, joy in
conjunction with others. " The best that hfe has to offer,"
he once exclaimed, " is a face glowing with happiness ! "

This look is expressed on his own face when he discusses
his ideals, above all the internationality of all intellectual
workers and the realization of eternal peace among the nations.
To him pacifism is a matter of mind as well as of heart, and he
is of the opinion that the course of history so far is but the
prelude to its reaUzation. The past, with its bloodstained
fingers that reach into the present, does not discourage him
He points to the endless city wars of the Middle Ages in Italy,
which had finally to cease in answer to the increasing feeling
of solidarity. So he believes in the victory of peace, which
the unified consciousness of all humanity will one day win over
the demonic powers of tyranny and conquest.

The pacifist ic goal seems to him to be attainable without the
pecuHarities of the various States being destroyed. National
characteristics arising from tradition and hereditary influences
do not signify in his eyes a contradiction to the internationalism
that embraces the common intellectual factors of civilized
peoples. Thus the desire for the preservation and care of
particularities directs him to the secondary goal of Zionism.
His blood asserts itself when he supports the foundation of a
State in Palestine, which seems to him to be the only means of
preserving the national individuaHty of his race without the
freedom of the individual being affected.

We had left Art to talk of the State, and then returned to
the former theme to touch lightly on the pictorial arts. Paint-
ing was allowed to pass with merely a fleeting remark. It
plays no considerable part in Einstein's existence, and he
would not suffer great grief if it were to vanish from the plane

240 EINSTEIN THE SEARCHER

of culture, a consummation to which definite signs seems to
point. I have described these signs in other writings (as in
Kunst in looo Jahren), and maintain the point of view that the
latest branches of painting as represented by expressionism and
cubistic futurism denote, in essence, the last convulsions of a
dying surface art . And even the chief representatives of former
flourishing periods are beginning to fade away, and Einstein will
not be the only one who will relegate this art, as compared with
music, to a lower plane among the inspired arts that bring joy
to humanity. He is only more frank than others when he
freely confesses that he cannot convince himself that a life
without the joys of pictorial art would be hopelessly impover-
ished. But he bows his head to sculpture, and, for him,
architecture is a goddess. It is again his deeply rooted piety
that asserts itself when memory recalls to him the Gothic dome
with its pinnacles striving towards heaven. Goethe and
Schlegel have called architecture " frozen music," and this
picture is present in his mind when he sees Gothic architecture
as frozen music of Bach. It is open to anyone to analyse this
specific impression in another way by seeking the fundamental
elements, in which the essence of the art is to provide support
for a weighty structure and to overcome gravitation. For a
spirit that works with mechanics and that feels within itself the
pressures and tensions occurring in external nature, archi-
tecture is a kind of statics and dynamics transformed into a
thing of beauty, a ravishing picture of his own science.

Einstein has told me many a story of his travels, and
these reports were characterized by an absence of definite
purpose. The conception of something worth seeing in the
tourists* sense does not exist for him, and he does not set out in
eager pursuit of those things that are marked with two asterisks
in Baedeker. The intense romanticism of Swiss scenery, that
lay within such easy reach for him, has never enticed him into
its magic circle, and he has nothing to do with the abysmal
terrors of glaciers and the world of snow-peaks. His en-
thusiasm for landscape beauty conforms ^\ith the behaviour of
the barometer : the greater the altitude, the lower the mercury.
In simple contact with Nature he prefers the lesser mountains,
the seashore, and extensive plains, whereas brilhant panoramic

EINSTEIN'S LIFE AND PERSONALITY 241

contours like those of the Vierwaldstetter See do not rouse
him into ecstasy. It is unnecessary to remark that he does
not arrange his Uving on the standard of the Grand Palace
Hotels en route. It is nearer the truth to picture him as a
vagrant who tramps along without a sense of time and without
a goal, in the fairy atmosphere of a joyous wanderer who has
unconsciously adopted the old rule of Philander : Walk with
a steady step : make your burden small : start early in the
morn, and leave home all care !

Am I to record the list of pleasures and hobbies that are
foreign to him ? The list would be very long, and I should
arrive at my goal more quickly by setting his sporting tendencies
equal to zero. I once suspected him of being given to aquatic
sport, as I learned that he had taken part in several yachting
excursions. But I was mistaken. He sails in the same way
as he walks on his tours, without a set purpose, dreaming, and
uninterested in what is regarded by members of sailing clubs
as a " feat." In the negative Hst of his games we see even
chess, that usually exerts a strong attraction on natures with
a mathematical tendency. The particular types of combina-
tion offered by this game have never tempted him, and the
world of chess has remained terra incognita for him. He is
just as Httle interested in every kind of collection, even that of
books. I have seldom or never met a savant who attaches so
Httle value to the personal possession of numerous and valuable
books. This statement may be extended as far as saying that
he experiences no pleasure at all in possession as such : he
says so himself, and his whole manner of life proves it. There
seems to me to be an element of resignation in his amiable
hedonism, a kind of monkish asceticism. He never rids him-
self of the feeling that he is only paying a visit in this world.

I do not know whether Einstein considers that his Ufe-
work can be completed within the span of this visit. At
any rate he makes no attempt to extract more out of the day
by following a rigid programme of work than the day volun-
tarily offers. He does not compel himself to cover a definitely
circumscribed piece of ground with chronological exactitude.
There are brain-workers, especially artists, who actually never
shake off the fetters of the twenty-four hours day of work
inasmuch as they spin on the threads of daily effort into the
i6

242 EINSTEIN THE SEARCHER

nightly fabric of dreams. Einstein can make a pause, inter-
rupt his work, or divert himself into side-channels at leisure
and according to the demands of the hour, but dreams offer
him no inspiration and do not waylay him with problems.

On the other hand, however, he is waylaid so much the
more during the day by things and persons that make an
assault on him. This starts as soon as the first post arrives,
to see through which requires a special bureau. In addition
to the communications of a professional or official nature
there appear innumerable letters from everywhere and any-
where asking him to grant a little of his time. Whaiever
each individual writer has thought about the principle of
relativity, all his thoughts and doubts, additions, and, above
all, that which he has not been able to understand, all this is
to be answered by Einstein. Has he, the child of fame, even a
quarter of an hour for himself ? There they wait in the hall,
the painter, the photographer, the sculptor, and the inter-
viewer ; with whatever powers of persuasion and argumenta-
tive subtlety his attentive wife may seek to defend his hours
of rest, some of these visitors will yet succeed in gaining the
upper hand, and will produce something in oil-colours, in
plaster of Paris, in black and white, in water-colours, or in
print. Fame, too, demands her sacrifices, and if we talk of a
hunt after fame, then Einstein is certainly not the hunter,
but the hunted.

He sighs under the burden of his correspondence, not only
as the recipient, but also with the sender, whose letter has to
remain unanswered. Yet he is never roused to anger by the
intruder on his time. If this were not so, the aphorism of
Cyrus that patience is the panacea of all ills would not hold
for him, and how would I myself otherwise have dared to
claim so many hours of him ? A sense of guilt falls on me !

But even Einstein's patience can come to an end, and this
is at the point where " society " begins : I mean the con-
gregation of persons in a salon, society entertainments to
which one is invited to be seen, and so that one may claim
to have been there. A solemn representation in which he is
to be made the cynosure of all eyes is a torture to him. If in a
very exceptional case he is compelled to participate in such a
gathering, the joy of his hosts will not be entirely unmixed.

EINSTEIN'S LIFE AND PERSONALITY 24S

for it does not require a thought -reader to recognize the longing
for solitude imprinted on his countenance : " Could I but
escape ! "

So much the happier does he feel himself in the narrow
circle of his friends, who offer what means to him much more
than admiration, namely, affection, and an appreciation of
his human self. He is what one wishes him to be. He is
happy when he can forget the doctor profundus, and can
yield himself up to the atmosphere of stimulating and un-
constrained converse. He is a master in the art of listening,
and is not averse to contradiction ; when possible, he even
emphasizes the arguments of his opponent. Audiatur et
altera pars ! This is a further manifestation of his altruistic
personality, which rejoices when he extracts the true kernel
from the husk of the opposing opinion. Here he also displays
a characteristic which one does not usually expect to find among
abstract thinkers, a sense of humour that runs through the
whole gamut from a gentle smile to hearty laughter, and that
is the happy source of many a striking sally. It may happen
that the subject of conversation excites his anger, especially
in political debates when he calls to mind militaristic or feudal
misgovernment. He then becomes roused, and, as a cynical
philosopher, sarcastically attacks personalities aind points out
the primary source of perennial hate, immediately afterwards
soaring up to happy speculations of the future.

It is a matter for regret that the subjects that he has
discoursed on lightly have not been fixed phonographically.
Such records would form an interesting supplement to the
conversations outlined in this book. It would never occur
to him to set down in permanent literary form the inspiration
of the moment. What he writes emanates from other regions,
and is, to use his own expression, a precipitate of " thick ink."
This is obvious, for what he has to proclaim as a scientist
cannot be presented in a " thin " form. But many a so-called
writer would have reason to congratulate himself, if so much
thinly flowing matter occurred to him in writing as to Einstein
in speaking.

The record of these conversations was begun in the summer of 1919, and
completed in the autumn of 1920.

INDEX

Aristoteles, 41
Arrhenius, 144

Babinet, 25
Bach, 88, 235
Bacon, 46

Baer, K. E. von, 162
Bailhaud, 144
Beethoven, 99, 234, 235
Bell, Graham, 25, iii
B6ranger, 84
Bergson, 91
Bernoulli, 48
Bernstein, 225
Bessel, 32

Bohr, Niels, 57, 210
Brahe, Tycho, 94
Bruno, Giordano, 141
Biichner, 225
Bulwer, 76
Bunsen, 164
Byron, 9

Cantor, 52, 203
Cavendish, iii
Ceulen, Ludolf van, 158
Condillac, 216
Copernicus, 6, 90
Cosmati, 48

Curie, Madame, 79, 231
Cuvier, 196

Darboux, 152
Dase, 158

Descartes, 47, 133, 162
Dingeldey, 190
Dostojewski, 185, 187
Dove, 21, 155
Duhem, 105, 106
Diihring, 54, 56

Eckermann, 50, 85
Edison, 140
Euclid, 180
Euler, 98
Euripides, 85

Faraday, 39. 61, 84
Fechner, no, 182

Fermat, 97, 190
Fizean, 113
Flammarion, 115
Franklin, 102
Fresnel, 45

Galilei, 6, 40, 150, 179, 181

Galle, 6

Galvani, no

Gauss, 55, 185, 186

Goethe, 13, 23, 179, 197, 212, 236

240
Grillparzer, 95
Grossmann, 229

Hansen, 134

Hebbel, 77, 86

Hegel, 42

Heine, 49

Helmholtz, 25, 26, 53, 73

Heraclitus, 23

Herschel, 84

Hertz, 60

Hooke, 41

Horace, 3

Humboldt, 49

Hume, 161

Huyghens, 56, 109, 132

Jean Paul, 86, 223

Joule, 84

Jung Stilling, 84

Kant. 35, 121, 170, 177, 179, 237
Kepler, 6, 42, 84, 176, 177
Kirchhoff, 104-7, 148, 212
Kleist, 130
Kummer, 190

Lamarck, 197

Lange, 47

Laplace, 40, 45, 140, 165

Leibniz, 26, 128

Leonardo da Vinci, 11, 50-54

Leverrier, 6, 10

Liebig, 55

Lindemann, 158

Linn6, 196

Lorentz, 57, 72

245

246

EINSTEIN THE SEARCHER

Lothar Meyer, 107
Lucretius, 210

Mach, 46, 77, 108, 149, 169
Mauthner, 95
Maxwell, 39, 60
Mayer, Robert, 25, 55, 56
Melanchthon, 82
Menander, 86
Mendelejew, 107
Mezzofanti, 63
Michelangelo, 49
Michelson and Morley, 112
Mill, 45

Mithridates, 63
Montaigne, 77
Mozart, 233

Newton, 2, 6, 8, 39, 40, 43, 96
Nietzsche, 63, 217, 237
I^ollet, 103

Odilon, Helene, 135
Oersted, 109
Ostwald, 83, 231, 232
Ovid, 197

Pascal, 93, 98

Pasteur, 175

Perrin, 154

Pfluger, 35

Philander, 241

Picard, 144

Planck, 57, 59, 91, 230

Poincar^, i, 7, 112, 116, 231

Pope, 54

Priestley, in

Psellus, 156

Pyrrhon, 92

Pythagoras, loi, 179

Quetelet, 182

Regiomantus, 52
Reis, 25
Riemann, 186
Riggenbach, 25
Ruess, 224
Rutherford, 36, 210

Schiller, 74, 94, 170
Schlegel, 240
Schlick, Moritz, 168
Schopenhauer, 41, 237
Schwann, 175
Shakespeare, 236
Siemens, 25, 27-30
Slade, 136
Sophocles, 238
Spinoza, 84, 162
Stephenson, 25

Terence, 191
Thomas Aquinas, 165
Torricelli, 166

Vaihinger, 45, 169
Vitruvius, loi
Volta, no. III
Voltaire, 47, 237

Wagner, 234
Weber, 182
Weierstrass, 152
Weyl, 34
Whewell, 45
Wien, 173

Zelter, 84
ZSllner, 137

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